Documents published in 2021 : Scipedia

Mixing and Combustion in Supersonic Near-Wall Shear Flows
R. Solomatin, I. Semenov, I. Menshov

WCCM-ECCOMAS2020.

Abstract
Mixing, ignition, and flame stabilization in a shear supersonic hydrogen-air flow is numerically studied with the RANS model of Spalart and Allmaras. A detailed chemical kinetics of hydrogen-air combustion is used in the calculations. The system of governing equations is solved with a hybrid explicit-implicit time marching scheme and the LUSGS method. Modelling of hydrogen injection into the M = 2.44 vitiated air flow in the model Burrows-Kurkov combustor is carried out for 2D and 3D cases. The numerical results obtained are compared with available experimental data.
Abstract
Mixing, ignition, and flame stabilization in a shear supersonic hydrogen-air flow is numerically studied with the RANS model of Spalart and Allmaras. A detailed chemical kinetics [...]
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Automatic and Sampling-Free Parametric Model Order Reduction of Vibro-Acoustic Systems
S. Ophem, E. Deckers, W. Desmet

WCCM-ECCOMAS2020.

Abstract
Recently, a novel parametric model order reduction formulation has been derived for vibroacoustic systems that allows for the reduction of systems with low-rank parametric changes [1]. This scheme does not require sampling of the parameter space, in contrast to conventional parametric model reduction techniques. This means that a single reduction basis, obtained with conventional non-parametric model order reduction schemes, can be used for a wide range of parameter values. This is done by rewriting the system in a non-parametric form, in which the low-rank contributions act as inputs. A disadvantage of this scheme is that the size of the input matrix scales with the amount of chosen parameters, leading to a potentially large reduced basis when many parameters are considered. Therefore, in [2] an automatic Krylov reduction scheme has been proposed that utilizes the similarity in the reduced bases for inputs which are spaced closely together to still get a small reduced basis with a large number of inputs. This is done by using a combination of block second order Arnoldi with a singular value decomposition acting on the resulting basis. The algorithm includes an error estimator that uses a complementary approximation to calculate the error. The main advantages of this algorithm as compared to the commonly used iterative rational Krylov approach [3] are that only a small amount of system inversions are required and that the final reduced order model has the desired predefined relative error in the specified frequency band. In this paper the automatic Krylov reduction scheme and low-rank parametric model order reduction approach are combined and a suitable error estimator is derived, to arrive at compact but accurate parametric reduced order models. The effectiveness is shown with several examples.
Abstract
Recently, a novel parametric model order reduction formulation has been derived for vibroacoustic systems that allows for the reduction of systems with low-rank parametric [...]
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Curvilinear Reconstructions for EBR Schemes On Semi-Structured Meshes
P. Rodionov

WCCM-ECCOMAS2020.

Abstract
The vertex-centered edge-based reconstruction (EBR) schemes for solving Eulertype equations are originally developed for tetrahedral unstructured meshes and imply the usage of quasi-one-dimensional straight-line reconstructions to calculate the flux. However, on the hybrid unstructured meshes with layers of highly anisotropic prismatic cells that are commonly used in simulations of turbulent flows with boundary layers, the straight-line reconstructions may lead to strongly irregular stencils, which cause both larger approximation errors and computational instabilities. To improve the accuracy and stability characteristics of EBR schemes on such meshes, we propose to use the curvilinear reconstructions for the flux computation. In this paper, we describe the principles and algorithms of constructing curvilinear reconstructions on the structured and semi-structured prismatic meshes. The modified EBR schemes are tested on the well-known NACA 0012 airfoil validation case for both two-dimensional and three-dimensional formulations, and the obtained numerical results are discussed in detail.
Abstract
The vertex-centered edge-based reconstruction (EBR) schemes for solving Eulertype equations are originally developed for tetrahedral unstructured meshes and imply the usage [...]
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Effects of Span Morphing on Flutter Characteristics of Subsonic Wing
D. DURMUŞ, M. KAYA

WCCM-ECCOMAS2020.

Abstract
This paper focuses on the dynamic behavior of variable-span morphing wings (VSMW) oscillating in pitch and plunge motions under subsonic flight conditions. The unswept cantilevered wing is modeled as three-stepped Euler-Bernoulli beam. The aerodynamic loads acting on the wing are represented by Theodorsen's unsteady aerodynamic theory. The differential equations of motion that describe the behavior of the dynamics of Euler-Bernoulli beam are derived through the Hamilton's principle. The differential transformation method (DTM) is implemented to equations of motion and boundary conditions. The solution of the aeroelastic system is obtained by the classical frequency domain solution, k-method. Goland wing and High-Altitude Long-Endurance (HALE) wing are used as the basis for this study. Prior to analyzing flutter characteristics of VSMW, validation cases are conducted to ensure that the developed algorithm works well. Furthermore, flutter speed and flutter frequency are analyzed for different elongation ratios of wing. There is a significant difference in flutter values of fully retracted and fully extended wing configurations. It can be concluded that both flutter speed and flutter frequency decrease dramatically as wing span extends. Another important finding is that the flutter speed and flutter frequency reductions are relatively high at the initial stages of wing span extension.
Abstract
This paper focuses on the dynamic behavior of variable-span morphing wings (VSMW) oscillating in pitch and plunge motions under subsonic flight conditions. The unswept cantilevered [...]
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An Electromechanical Micropolar Peridynamic Model for Isotropic and Orthotropic Materials
V. Diana, V. Carvelli

WCCM-ECCOMAS2020.

Abstract
A micropolar peridynamic model for in-plane electro-mechanical behavior of isotropic and orthotropic solids is presented. The analytical implicit formulation of the electrical part of the model is based on the definition of a proper microelectrical energy function and a specific electrical inelastic deformation parameter. A compatibility condition and a constitutive relationship has been derived and thus the electrical stiffness operator has been obtained. The electrical formulation is then coupled with a mechanical micropolar peridynamic formulation that accounts for full orthotropy and isotropy as special case. A distinctive aspect of the formulation is the use of continuous trigonometric functions, for the mechanical and electrical bond properties with respect to the principal material axes. The obtained unified model is capable to predict the mechanical response and the electrical conduction of elastic brittle materials taking into account the influence of cracks and other defects along with mechanical and/or electrical orthotropy. The proposed model has been applied to predict the electric field potential in isotropic and orthotropic square laminae, and to simulate a coupled electromechanical problem.
Abstract
A micropolar peridynamic model for in-plane electro-mechanical behavior of isotropic and orthotropic solids is presented. The analytical implicit formulation of the electrical [...]
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Mathematical Modeling of Thermal Ablation Treatments in Heart Arrhythmias
A. Amatriain, I. Parra, G. Rubio, E. Valero

WCCM-ECCOMAS2020.

Abstract
In this work we develop a model of catheter ablation based on electromagnetic and thermal equations. This model allows the computation of the space and time evolution of temperature in the surroundings of the ablation zone. This result is relevant, as excessive temperature values may cause stream pops or esophageal ulcers. The resulting system of equations is solved using a Chebyshev spectral collocation method. Special attention is paid to the effect of blood perfusion and electrical conductivity, as there is no consensus in the literature concerning the modeling of these terms. In order to obtain the conditions that give rise to safer ablations, a parametric study is performed, where the effect of discharge time, discharge voltage and size of the electrode in the temperature distribution is analysed.
Abstract
In this work we develop a model of catheter ablation based on electromagnetic and thermal equations. This model allows the computation of the space and time evolution of temperature [...]
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MHD Stability in Aluminium Electrolysis Cells – From Complex to Simple Analysis
V. Bojarevics

WCCM-ECCOMAS2020.

Abstract
Numerical modelling has become a primary tool for design and optimization of commercial high amperage aluminium electrolysis cells. The design of industrial cells requires to account for a variety of their individual features: bus-bar network, cell bottom profile and side ledge, cathode bar design, ferromagnetic parts effect, operational adjustments due to the anode changes, etc. Analytical solutions in special cases provide benchmark tests and aid understanding of the basic physics. The commercial Trimet cell is analyzed using a simple theoretical, full numerical and advanced analytical problem solutions, which are compared with experimental measurements using wireless sensors to detect MHD instability onset.
Abstract
Numerical modelling has become a primary tool for design and optimization of commercial high amperage aluminium electrolysis cells. The design of industrial cells requires [...]
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An Unstructured Shock-Fitting Technique For Three-Dimensional Flows With Shock Interactions
C. Ollivier-Gooch, R. Paciorri, A. Assonitis, A. Bonfiglioli

WCCM-ECCOMAS2020.

Abstract
The numerical simulation of hypersonic flows past blunt bodies by means of shockcapturing (S-C) solvers is characterized by some critical challenges, including: stagnation point anomalies, spurious numerical oscillations, the carbuncle phenomenon and the reduction of the order of accuracy of the solution in the entire region downstream of a captured shock worsen the solution quality. This paper describes an updated version of the unstructured shock-fitting (S-F) algorithm for three-dimensional flows. In particular, we present a comparison between the results obtained computing hypersonic flows on blunt bodies using both the S-C and S-F techniques on nearly identical tetrahedral meshes, with a special interest on the grid-convergence properties of the two different shock-modeling options.
Abstract
The numerical simulation of hypersonic flows past blunt bodies by means of shockcapturing (S-C) solvers is characterized by some critical challenges, including: stagnation [...]
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A Probabilistic Approach In Long-Term Fatigue Analysis Of Onshore Wind Turbine Tower
H. Bai, D. Lemosse, Y. Aoues, J. Cherfils, C. Huang

WCCM-ECCOMAS2020.

Abstract
To address the fatigue damage induced by wind on the wind turbine tower, the present work introduces a novel probabilistic fatigue assessment framework. The idea is based on the deterministic fatigue approach combining with various statistical and probabilistic techniques. The proposed framework is applied to a Design Load Case (DLC) given in IEC 61400-1 standard using a reference wind turbine and carry out a probability distribution of cumulative fatigue damage on the cross-section of wind turbine tower under a turbulent wind condition.
Abstract
To address the fatigue damage induced by wind on the wind turbine tower, the present work introduces a novel probabilistic fatigue assessment framework. The idea is based [...]
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Geomiso TNL: A Software for Non-Linear Static T-Spline-Based Isogeometric Analysis of Complex Multi-Patch Structures
P. Karakitsios, G. Karaiskos, A. Leontaris, P. Kolios

WCCM-ECCOMAS2020.

Abstract
A new software, Geomiso TNL, is proposed to facilitate the use of isogeometric analysis and 3D design with NURBS and T-splines. Its dual nature eliminates geometric errors by merging geometric design with mesh generation into a single procedure. It is based on the isogeometric method, the powerful generalization of the traditional finite element method. This paper presents four sample applications in non-linear solid and structural mechanics. This software is seen to handle these situations remarkably well, as the numerical examples exhibit significantly improved accuracy of the results, such as displacement, strain and stress fields, and reduced computational cost when compared with finite element analysis. It is argued that Geomiso TNL is a new, more efficient, alternative to finite element software packages and possesses several advantages.
Abstract
A new software, Geomiso TNL, is proposed to facilitate the use of isogeometric analysis and 3D design with NURBS and T-splines. Its dual nature eliminates geometric errors [...]
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A Non-Intrusive Reduced Basis Method for Urban Flows Simulation
R. Chakir, B. Streichenberger, P. Chatellier

WCCM-ECCOMAS2020.

Abstract
In this work, we present a non-intrusive method using the Reduced Basis framework in order to diminish the cost of numerical simulation arising from the computation of parameters-dependent Partial Differential Equations (PDE). This method involves the computation of less expensive (but less accurate) solutions of the PDE during the online stage, and a RB-based rectification step. It represents a good substitute for standard Reduced Basis methods when it is applied to urban flows modelling. This approach speeds up the CFD simulation while remaining non-intrusive in relation to the high fidelity model, which can allow to avoid practical problems (e.g. non-affine parametric dependence) associated to model reduction for complex air flows involved in many sophisticated methods of urban air quality modeling. Our focus here is on the validation of the non-intrusive method applied to the backward-facing step 2D benchmark.
Abstract
In this work, we present a non-intrusive method using the Reduced Basis framework in order to diminish the cost of numerical simulation arising from the computation of parameters-dependent [...]
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Adaptive Topology Optimization for Innovative 3D Printed Metamaterials
D. Cristofaro, C. Galimberti, D. Bianchi, R. Ferrante, N. Ferro, M. Mannisi, S. Perotto

WCCM-ECCOMAS2020.

Abstract
An adaptive method for designing the infill pattern of 3D printed objects is proposed. In particular, new unit cells for metamaterials are designed in order to match prescribed mechanical specifications. To this aim, we resort to topology optimization at the microscale driven by an inverse homogenization to guarantee the desired properties at the macroscale. The whole procedure is additionally enriched with an anisotropic adaptive generation of the computational mesh. The proposed algorithm is first numerically verified both in a monoand in a multi-objective context. Then, a mechanical validation and 3D manufacturing through fused-model-deposition are carried out to assess the feasibility of the proposed design workflow.
Abstract
An adaptive method for designing the infill pattern of 3D printed objects is proposed. In particular, new unit cells for metamaterials are designed in order to match prescribed [...]
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Simulating Compressible and Nearly-Incompressible Linear Elasticity Using an Efficient Parallel Scalable Matrix-Free High-Order Finite Element Method
A. Mehraban, J. Thompson, J. Brown, R. Regueiro, V. Barra, H. Tufo

WCCM-ECCOMAS2020.

Abstract
We examine a residual and matrix-free Jacobian formulation of compressible and nearly incompressible (v → 0.5) displacement-only linear isotropic elasticity with high-order hexahedral finite elements. A matrix-free p-multigrid method is combined with algebraic multigrid on the assembled sparse coarse grid matrix to provide an effective preconditioner. The software is verified with the method of manufactured solutions. We explore convergence to a predetermined L2 error of 10-4, 10-5 and 10-6 for the compressible case and 10-4, 10-5 for the nearly-incompressible cases, as the Poisson's ratio approaches 0.5, based upon grid resolution and polynomial order. We compare our results against results obtained from C3D20H mixed/hybrid element available in the commercial finite element software ABAQUS that is quadratic in displacement and linear in pressure. We determine, for the same problem size, that our matrix-free approach for displacement-only implementation is faster and more efficient for quadratic elements compared to the C3D20H element from ABAQUS that is specially designed to handle nearly-incompressible and incompressible elasticity problems. However, as we approach the near incompressibility limit, the number of Conjugate Gradient iterations required to achieve the desired solution increases significantly.
Abstract
We examine a residual and matrix-free Jacobian formulation of compressible and nearly incompressible (v → 0.5) displacement-only linear isotropic elasticity [...]
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Comparison of Monolithic and Partitioned Approaches for Ponding Analysis On Membrane Structures
N. Narayanan, R. Wüchner, J. Degroote

WCCM-ECCOMAS2020.

Abstract
Membrane structures are vulnerable to ponding due to their large deformation characteristic. The ponding on membrane structures is usually caused by rainfall on an already deformed structure due to a seeding event such as snow accumulation. This paper discusses two monolithic methods and a partitioned method for determining the static deformation of the membrane structure due to a given volume of ponding water. The monolithic methods involve simultaneously solving the structural equations and the fluid equations under static conditions, to obtain the structural deformation. The partitioned method on the other hand involves external coupling iterations involving a structural solver and volume conserving solver, where the volume conserving solver is responsible for updating the free surface to maintain a given volume of water. The discussed methods are compared in terms of robustness and computing time. It was found that the monolithic methods were computationally efficient. However, the partitioned method-apart from being modular-was found to be more robust with quasi-Newton convergence accelerators.
Abstract
Membrane structures are vulnerable to ponding due to their large deformation characteristic. The ponding on membrane structures is usually caused by rainfall on an already [...]
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Modified Spectral Method of Anisotropic Turbulent Velocity Field Generation Preserving Incompressibility
A. Alexandrov, L. Dorodnicyn, A. Duben, D. Kolyukhin

WCCM-ECCOMAS2020.

Abstract
A method for the numerical generation of anisotropic turbulent velocity fields is presented. The proposed technique is based on the spectral method (SM) [1]. The traditional adaptation of isotropic field generated with spectral methods uses a Cholesky decomposition of Reynolds stresses tensor. After this adaptation the resulted field loses the property of incompressibility provided in the isotropic case. We have modified this method to use it in the anisotropic case and guarantee the incompressibility of generated turbulent field. Comparison of the results of IDDES simulation of canonical turbulent flow using inlet boundary conditions based on modified and non modified spectral methods are presented.
Abstract
A method for the numerical generation of anisotropic turbulent velocity fields is presented. The proposed technique is based on the spectral method (SM) [1]. The traditional [...]
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Accuracy Assessment of Finite-Volume and High-Order Compact Methods for LES of Combustor Flow-Fields
V. Saini, H. Xia, G. Page

WCCM-ECCOMAS2020.

Abstract
The Large-Eddy Simulations (LES) play an important role in the study and design of gas turbine combustors. In order to bring the cost of LES down, compact high-order accurate solvers that can handle complex geometry are a promising method. However, their accuracy vs cost benefit as compared to the standard finite-volume solvers is unclear when it comes to under-resolved hybrid unstructured meshes. These meshes are required to represent the industrial combustor geometries. In this work, a high-order spectral/hp (Nektar++) solver is compared to a standard finite-volume (OpenFoam) solver for a fixed cost. Two combustor-relevant configurations are employed, port-flow and swirling flow. It is found that high-order solver provides moderate accuracy improvements in terms of the mean results and significant improvements for the unsteady results.
Abstract
The Large-Eddy Simulations (LES) play an important role in the study and design of gas turbine combustors. In order to bring the cost of LES down, compact high-order accurate [...]
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Application of Artificial Neural Network for Fatigue Analysis in Wind Turbine Blade
W. Veloz, H. Bai, Y. Aoues, D. Lemosse

WCCM-ECCOMAS2020.

Abstract
Wind turbine blades are subjected to wind pressure distribution that depends on the external environment and the inertial loads from their rotational velocity, acceleration, and turbine control. To simulate these effects, numerical tools are used. Allowing a coupled nonlinear aero-hydro-servo-elastic simulation in the time domain representing the multibody 1D beam finite element model (FEM). Nevertheless, when the mechanical analysis comes into detail, a shell FEM with applied loads in 3D spatial space must be used to analyze the fatigue. Therefore, the loads estimated by beam simulations need to be transferred into an equivalent 3D distributed loads for the shell FEM Called in the literature Load Application Methods (LAM), Each of these LAM differs in the stress distribution and the deflection of the blade. Subsequently, fatigue analysis of the whole blade can be performed by defining the cycle counting method and multi-axial damage criteria for composite material. However, this process is computationally expensive, since it is required to calculate the stress history in the shell FEM of the blade for each time instant of the aero-elastic simulation for different mean wind speed, other authors use a damage equivalent load (DEL) to estimate the fatigue damage directly from the 1D simulations. To reduce the number of call of the aero-elastic and shell FEM simulation a deep neural network (DNN) was trained to predict the accumulated fatigue damage in a node of the blade given the 10 minutes mean wind speed and the empirical cumulative density function of the damage per cycles with a relative error less than 5%
Abstract
Wind turbine blades are subjected to wind pressure distribution that depends on the external environment and the inertial loads from their rotational velocity, acceleration, [...]
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An Isogeometric Solid-Shell Model for Postbuckling Optimisation Strategies
F. Liguori, A. Madeo, L. Leonetti, D. Magisano, G. Garcea

WCCM-ECCOMAS2020.

Abstract
The optimal design of shell structures undergoing buckling phenomena is nowadays an open problem, whose solution would provide interesting answers to both academy and industry. The main difficulty is represented by the high computational cost required for optimising a full-scale structure characterised by a relatively complex postbuckling behaviour. In this work, this topic is addressed by proposing an isogeometric solid-shell model. The equilibrium path is evaluated through a multimodal Koiter's method. The resulting postbuckling analysis turns out to be efficient and accurate, as shown by numerical examples.
Abstract
The optimal design of shell structures undergoing buckling phenomena is nowadays an open problem, whose solution would provide interesting answers to both academy and industry. [...]
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Controlling Nonlinear Elastic Systems in Structural Dynamics
T. Ströhle, P. Betsch

WCCM-ECCOMAS2020.

Abstract
This contribution deals with the feedforward control of continuous mechanical systems. After introducing a general formulation of such problems and adressing the limitations of the commonly used semi-discrete method, two numerical methods are presented that resolve these limitations.
Abstract
This contribution deals with the feedforward control of continuous mechanical systems. After introducing a general formulation of such problems and adressing the limitations [...]
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A Numerical Multiscale Method for Fiber Networks
M. Görtz, G. Kettil, A. Målqvist, A. Mark, F. Edelvik

WCCM-ECCOMAS2020.

Abstract
Fiber network modeling can be used for studying mechanical properties of paper [1]. The individual fibers and the bonds in-between constitute a detailed representation of the material. However, detailed microscale fiber network models must be resolved with efficient numerical methods. In this work, a numerical multiscale method for discrete network models is proposed that is based on the localized orthogonal decomposition method [4]. The method is ideal for these network problems, because it reduces the maximum size of the problem, it is suitable for parallelization, and it can effectively solve fracture propagation. The problem analyzed in this work is the nodal displacement of a fiber network given an applied load. This problem is formulated as a linear system that is solved by using the aforementioned multiscale method. To solve the linear system, the multiscale method constructs a low-dimensional solution space with good approximation properties [5, 2]. The method is observed to work well for unstructured fiber networks, with optimal rates of convergence obtainable for highly localized configurations of the method.
Abstract
Fiber network modeling can be used for studying mechanical properties of paper [1]. The individual fibers and the bonds in-between constitute a detailed representation of [...]
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Coupled Multiphysics Modeling of Aortic Dissection
R. Schussnig, T. Fries

WCCM-ECCOMAS2020.

Abstract
Computational modeling of the cardiovascular system plays an increasingly important role in biomedicine, as it allows for non-invasive investigations of the status-quo and studying the influence of different treatment options available. The goal is to incorporate patient-specific datasets to obtain socalled digital twins to increase relevance of virtual surgery and support clinical decision making. In this context, aortic dissection is particularly challenging, since the overall system behavior strongly depends on the interplay between tissue deformation and blood flow, giving rise to a fully coupled fluid-structure interaction problem. To account for the complex physics, several additional modeling aspects such as prestress, advanced constitutive models respecting fibre orientation and suitable boundary conditions for the fluid and solid phases have to be considered. Within this study, these special techniques are applied to a patient-specific dataset, for which first results are presented highlighting their relevance.
Abstract
Computational modeling of the cardiovascular system plays an increasingly important role in biomedicine, as it allows for non-invasive investigations of the status-quo and [...]
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Autonomous Cooking with Digital Twin Methodology
M. Kannapinn, M. Schäfer

WCCM-ECCOMAS2020.

Abstract
This work introduces the concept of an autonomous cooking process based on Digital Twin methodology. It proposes a hybrid approach of physics-based full order simulations followed by a data-driven system identification process with low errors. It makes faster-thanreal-time simulations of Digital Twins feasible on a device level, without the need for cloud or high-performance computing. The concept is universally applicable to various physical processes.
Abstract
This work introduces the concept of an autonomous cooking process based on Digital Twin methodology. It proposes a hybrid approach of physics-based full order simulations [...]
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Using Computed Tomography Data for Finite Element Models of Wood Boards
J. Huber, M. Ekevad, O. Broman

WCCM-ECCOMAS2020.

Abstract
A procedure is presented to generate 3D FE models of timber boards based on CT scans. The boards were tested in four-point bending tests until failure and the local displacement in the pure bending zone was recorded. The CT scans were treated as 3D images and image processing methods were used to reconstruct the board, the knots and the pith. A new procedure to reconstruct the fibre deviations around knots by accounting for image gradient information was used. A quadratic tetrahedral mesh was generated for the region of the board which was under pure bending in the tests. The fibre directions and the stiffness tensor, scaled by the local density, were transferred into each integration point of the mesh and the bending test was replicated. Preliminary results show that the procedure is able to realistically predict the observed local stiffness of the boards. Further development of the procedure is required to account for dead knots and to extend the procedure for indicating strength and predicting failure.
Abstract
A procedure is presented to generate 3D FE models of timber boards based on CT scans. The boards were tested in four-point bending tests until failure and the local displacement [...]
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Disciplinary Implications of a System Architecting Approach to Collaborative Aircraft Design
J. Walther, P. Ciampa, B. Nagel

WCCM-ECCOMAS2020.

Abstract
In the face of growing public awareness of environmental issues such as climate change, the pressure to provide efficient and ecological new air transport solutions is higher than ever on the aviation community. To this aim, unconventional aircraft configurations, which are radically different from the established tube-and-wing architecture, may hold a lot of potential [1]. However, OEMs today usually shy away from such configurations due to the significantly increased uncertainty and entrepreneurial risk connected to such drastic design changes. In order to reduce the risk and increase knowledge about a new configuration, the application of physics-based analyses on a virtual aircraft can add significant value, when applied in the early stages of the design process by bringing new technologies to higher TRLs quickly. Due to the highly multidisciplinary nature of the aircraft design task, the success of this approach largely depends not only on the well-organized handling of the available product data at any point in the design process but also the smart sequencing of the disciplinary contributions based on their mutual dependencies. In this paper, a methodology for an integrated and collaborative approach to preliminary aircraft design is presented. It applies several well established components, such as CPACS (Common Parametric Aircraft Configuration Schema) [2] as a central product data schema and RCE (Remote Component Environment) [3] which enables an automated collaborative approach to aircraft design and combines them with methods from system architecting and model-based engineering [4]. Furthermore, the requirements for a disciplinary analysis and design tool to contribute to an integrated multidisciplinary design process are highlighted. Three examples are given, assuming the perspective of a structural designer: · An unmanned aerial vehicle from the AGILE project [4], where a cross-organizational workflow has been set up in order to perform aero-structural MDO on the wing planform [5]. · A Prandtl-plane configuration from the Parsifal project [6]. Here, a tail plane design and sizing is performed using data collected from a variety of partners. · A conventional configuration from the InDiCaD project, where the structural layout is designed in tandem with the cabin [7, 8]. The example cases demonstrate the initial investment necessary in order to integrate a disciplinary tool into a multidisciplinary environment as well as the potential benefits of being able to perform the analysis within a larger context.
Abstract
In the face of growing public awareness of environmental issues such as climate change, the pressure to provide efficient and ecological new air transport solutions is higher [...]
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A Dem Model to Predict and Correct Spreader Shear-Induced Part Deformation in Binder Jet Additive Manufacturing
P. Desai, C. III

WCCM-ECCOMAS2020.

Abstract
Powder bed additive manufacturing (AM) is comprised of two repetitive steps: spreading of powder and selective fusing or binding the spread layer. Powder-bed AM can be sub-categorized as fusion-based where electron beams or laser beams are used to fuse the spread powder layer and binder-based where a liquid binder is used to bind the spread layer at areas specified by the governing CAD model. The latter process, commonly referred to as binder jet additive manufacturing (BJAM), outperforms fusion-based methods with respect to cost, build time, and material suitability; however, the parts are prone to shear-induced deformation during the powder spreading stage. Unlike fusionbased AM, the strength of BJAM parts is not fully developed until sintering and infiltration during postprocessing. This results in BJAM parts being more susceptible to deformation or even breakage due to the shearing action of the spreader. This shear-induced deformation can affect the precision and thereby performance of 3D printed parts. The binding step in BJAM is a complex function of binder viscosity, density, droplet size, impact speed, and drying time. The spreading step is a complex function of spreader speed and spreader shape, topography of spread and bound layer, and the rheology of the AM powder. This study presents a first-order model to simulate BJAM using a weak concrete-like, non-local, multilayer bonded DEM model. The DEM model has been parallelized using the massive parallelism offered by GPUs. An industry-grade metal powder is used to print physical cuboids at varying spreader speeds. The model is qualitatively verified against experiments on a real 3D printer. The model can be used to provide layer-wise spreading process control to minimize spreader shear-induced deformations.
Abstract
Powder bed additive manufacturing (AM) is comprised of two repetitive steps: spreading of powder and selective fusing or binding the spread layer. Powder-bed AM can be sub-categorized [...]
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An Extended Technique for Computation of Laplace Transformed Dynamic Fundamental Solutions for 3D Anisotropic Elastic Solids
I. Markov, S. Litvinchuk, A. Belov

WCCM-ECCOMAS2020.

Abstract
This paper presents an extended procedure for computation of integral representations of regular parts of Laplace domain three-dimensional dynamic anisotropic elastic full space displacement fundamental solutions and their spatial derivatives. The problem is that under specific conditions these integrals become highly oscillatory. For the modified integral expressions, we present a technique that utilizes specialized quadrature rule which in turn is a variation of well-known Levin's method for solving highly oscillatory integrals. Results of numerical investigations suggest improved performance (regarding number of integration points) compared to using the Gauss-Legendre quadrature.
Abstract
This paper presents an extended procedure for computation of integral representations of regular parts of Laplace domain three-dimensional dynamic anisotropic elastic full [...]
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Ontologies In Computational Engineering
H. Preisig, T. Hagelien, J. Friis, P. Klein, N. Konchakova

WCCM-ECCOMAS2020.

Abstract
Industry and science define traditionally many needs for simulations. So one may ask what can be new in a field that is so well covered over so many years. It is not only the computing hardware that has undergone revolutionary developments. In parallel, software engineering kept pace more and more high-level abstractions make their way into technology, making software systems increasingly powerful. The industry has an increasing need for multidisciplinary simulation, thereby generating demand for an extension towards integrating more different disciplines. Ontologies provide a perfect vehicle for the representation and coupling of knowledge, thus the integration. So the aim is to introduce ontologies on all levels into the larger domain of simulation software systems and construct a generic simulation ontology-based framework. The approach is focused on business-decisions and translation support using layers of simulation tools, including multiscale systems simulations of physics-based models. Latter describes the processing units' internals being coupled with control, optimisation and performance analysis based on ecology and techno-economical criteria.
Abstract
Industry and science define traditionally many needs for simulations. So one may ask what can be new in a field that is so well covered over so many years. It is not only [...]
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Verification of BDF Time-Integration Method with Variable Step Size
C. Klaij

WCCM-ECCOMAS2020.

Abstract
Solution methods for systems of ordinary differential equations with variable step size base their choice for the step size on (an estimate of) the local truncation error. Significant savings in computational effort can be obtained as the step size is only refined when necessary. We first summarize the information that is needed for a variable step size BDF2 method in a way that is directly suitable for implementation in an existing code. We then propose a solution verification procedure that does not require direct control of the step size to carry out refinement studies and apply it to a textbook example. Finally, we explore the use of the variable step size BDF2 method for time integration of the NavierStokes equations in the CFD package REFRESCO and find plausible results for vortex shedding in the wake of a cylinder, but no major savings for this particular case.
Abstract
Solution methods for systems of ordinary differential equations with variable step size base their choice for the step size on (an estimate of) the local truncation error. [...]
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Surface Elasticity for Applications to Material Modelling at Small Scales
L. Igumnov, V. Eremeyev, A. Ipatov, A. Bragov

WCCM-ECCOMAS2020.

Abstract
We discuss the various applications of the surface elasticity to determination of effective properties of materials and some related phenomena as surface wave propagation. In the frame of surface elasticity in addition to the constitutive relations in the bulk we independently introduce constitutive relations at the surface. Nowadays the most popular models of surface elasticity relates to the models by Gurtin and Murdoch and by Steigmann and Ogden. First we discuss some useful surface elasticity models. The corresponding boundary dynamic boundary conditions are derived at the smooth parts of the boundary as well as at edges and corner points. Let us underline that these conditions include also dynamic terms. As a result, we have here a dynamic generalization of the Laplace-Young equation known from the theory of capillarity. Second, we discuss the influence of the surface stresses at the effective stiffness parameters of layered plates and shallow shells. For small deformations we derived the exact formulae for modified tangent and bending stiffness parameters of the plates and shells. The influence of residual surface stresses is also discussed. Unlike to previous case where surface stresses are slightly changing the material properties, there is another example of essential influence of surface properties. This example relates to the propagation of anti-plane surface waves. We discuss some peculiarities of the wave propagation.
Abstract
We discuss the various applications of the surface elasticity to determination of effective properties of materials and some related phenomena as surface wave propagation. [...]
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Simulation of Frictional Contact Interactions Between Warp Yarns and Heddles Within Jacquard Harness for 3d Weaving
S. Mermouli, P. Sorbo, D. Durville, B. Tranquart, D. Coupé

WCCM-ECCOMAS2020.

Abstract
The relative motions between warp yarns and heddles within the Jacquard harness used for 3D weaving induce frictional interactions between these elements which may generate both damage in the yarns and weaving errors. To identify the interaction phenomena taking place within such harnesses, a finite element model, based on an implicit solution scheme [1], is proposed. In this model, all elements involved in the harness (cords, heddles, warp yarns) are represented using finite strain beam elements, and frictional contact elements are automatically created to account for frictional contact interactions. Motions defined by the Jacquard card for the shedding are prescribed as boundary conditions to the upper ends of the heddles. The resultant forces necessary to move the heddles are obtained as results of the simulation. Simulation results for an interlock fabric, with 28 warp yarns, will be presented, showing the forces evolution applied to the heddles over a few dozen consecutive sheddings.
Abstract
The relative motions between warp yarns and heddles within the Jacquard harness used for 3D weaving induce frictional interactions between these elements which may generate [...]
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Defects Location Estimation Using Multiscale Thermal Finite Element Method
Y. Bresson, A. Tongne, L. Arnaud, M. Baili

WCCM-ECCOMAS2020.

Abstract
The Selective Laser Melting (SLM) process is the subject of numerous researches for a few decades. Manufactured parts experience very high heating and cooling rates along the laser beam path and suffer an extensive range of temperatures. These high heating and cooling rates can lead to defects such as cracks, distortions, and porosities. These defects are driven by the thermal history, related to several factors such as scanning strategy, surrounding powder insulation, parts geometry, number of parts to be manufactured, recoating time, etc. All these factors need to be considered to precisely simulate the thermal history. In this study, a multiscale thermal approach has been developed and applied to a study case. Most of the thermal history aspects are covered using five temporal and spatial scales FEM model. The overall thermal history and future improvements for simulating a full build plate in reasonable computational time are discussed.
Abstract
The Selective Laser Melting (SLM) process is the subject of numerous researches for a few decades. Manufactured parts experience very high heating and cooling rates along [...]
- 34
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Numerical Simulation of Heavy Oil Recovery by Steam-Assisted Gravity Drainage Method
A. Kostina, M. Zhelnin, O. Plekhov

WCCM-ECCOMAS2020.

Abstract
Steam-assisted gravity drainage method (SAGD) is an efficient technique for a heavy oil recovery which is characterized by values of recovery factor up to 0.8. This work is devoted to the three-dimensional field-scale numerical simulation of SAGD taking into account various kind of non-uniformity induced by technological reasons as well as heterogeneous structure of the reservoir. The proposed coupled thermo-hydro-mechanical model includes conservation laws of momentum, mass and energy which are supplemented by constitutive equations and state laws. Results have shown that oil production rate is significantly affected by the presence of the barrier layers as well as non-uniformity of the steam propagation along the horizontal wellbore.
Abstract
Steam-assisted gravity drainage method (SAGD) is an efficient technique for a heavy oil recovery which is characterized by values of recovery factor up to 0.8. This work is [...]
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On the Thermodynamics of Dynamic Recrystallization for Viscoplasticity at Large Strains
H. Westermann, R. Mahnken

WCCM-ECCOMAS2020.

Abstract
During the thermo-mechanical processing of metals, complex microstructure evolution inevitably occur, altering the marcoscopic material properties. The vital microstructure mechanisms include viscoplastic deformation, dynamic recovery (DRV) and dynamic recrystallization (DRX), leading to the hardening and softening of the material. A thermodynamic framework for dynamic recrystallization is proposed covering the state in crystalline materials. Several improvements are presented for an internal state variable (ISV) model to consider the evolution of dislocations dependent on recrystallized volume fractions and derive the constitutive relations for microscopic and macroscopic quantities coupled to viscoplasticity. The relation between microscopic quantities and the macroscopic hardening stress is clarified based on thermodynamic arguments and thermodynamic consistency is derived. On the numerical side a suitable explicit/implicit algorithm is presented and the evolution equations are validated based on experimental data for OFHC copper. During parameter identification the material parameters are determined solving the inverse problem. In numerical examples the constitutive equations are applied to simulations for uniaxial loading and the characteristics of continuous dynamic recrystallization such as strain softening are illustrated.
Abstract
During the thermo-mechanical processing of metals, complex microstructure evolution inevitably occur, altering the marcoscopic material properties. The vital microstructure [...]
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Numerical Simulation of Wood-Polymer Composites Extrusion
F. Liese, O. Wünsch, S. Yatsenko, J. Rudloff, M. Lang, T. Hochrein, M. Bastian

WCCM-ECCOMAS2020.

Abstract
The combination of fillers and polymers is used to influence the mechanical, optical and processing properties of the base material and is finding more and more applications. The addition of wood to polymers results in wood-polymer composites (WPC), whereby the wood content can be up to 80 wt. %. This composite is mainly processed to deckings by means of extrusion. The extrusion die is an essential part of the processing procedure, which determines both process parameters and the final product. A special feature of WPC extrusion dies is cooling plate, which leads to partial solidification of the melt before leaving the die. This solidification is necessary to ensure dimensionally stable extrusion without strand breakage. For the design of WPC extrusion dies, numerical simulations are increasingly used in addition to empirical data, whereby OpenFOAM is used in the present investigations. Based on rheological measurements, both the shear thinning flow behavior and the temperature dependence of the viscosity are modeled. The partial solidification of the melt at the cooling plate before the outlet is modeled in a single-phase over a step in viscosity. In addition, the solidified melt slips on the cooling wall, which is also taken into account in the model. In the parallel zone, there is a pure shear flow, while in the transition elements such as the flange to the extruder or at the mandrel, uniand biaxial extension components are dominant due to the crosssectional changes. High-density polyethylen (HDPE) with wood flour exibits a shear thinning and extensional thickening behavior, so that different models are necessary for description. To calculate the stresses, interpolation is performed between the different models with respect to the invariants according to B¨ohme [1], depending on the type of flow present. To validate the numerical simulations, an extrusion die for a square hollow profile with pressure and temperature sensors along the flow direction is subject to experimental measurements. The aim of the numerical simulations is to investigate the flow in more detail and to give optimization hints.
Abstract
The combination of fillers and polymers is used to influence the mechanical, optical and processing properties of the base material and is finding more and more applications. [...]
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Numerically Analyzing Nonlinear Dynamic Deformation and Loss of Stability of Prestressed Composite Cylindrical Shells
L. Igumnov, N. Abrosimov, A. Еlesin, N. Dyukina

WCCM-ECCOMAS2020.

Abstract
Within the framework of the applied shell theory, an energetically consistent resolving system of equations is formulated and a complex numerical method is developed that allows solving both quasi-static and dynamic problems of nonlinear non-axisymmetric deformation and loss of stability of composite cylindrical shells within the framework of an explicit variational-difference scheme. The reliability and accuracy of the proposed method are justified by comparing numerical calculations with experimental data. For various reinforcement structures, the analysis of the characteristic spatial configurations and critical loads of the loss of stability of fiberglass cylindrical shells is carried out, depending on the amount of preloading by quasi-static internal pressure and subsequent loading by axial dynamic compression.
Abstract
Within the framework of the applied shell theory, an energetically consistent resolving system of equations is formulated and a complex numerical method is developed that [...]
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Mixed Finite Element Formulations for Polyconvex Anisotropic Material Formulations
J. Dietzsch, M. Groß

WCCM-ECCOMAS2020.

Abstract
Our research activity takes place within the research project GR 3297/4, funded by `Deutsche Forschungsgemeinschaft' (DFG), and aims at a robust simulation method for fiber-reinforced materials in light-weight structures. One goal is to avoid looking-effects in the static and dynamic regime, which occur due to nearly incompressible matrix materials and highly stiff fibers. Therefore, we extend the mixed finite elment formulations, hown in References [1, 2, 3]. In the description of the material behavior, we also use polyconvex strain energy functions [4]. In case of the so-called CoFEM element in Reference [2], the volumetric dilatation and the cofactor of the right Cauchy-Green tensor are approximated independently beside the displacement. In Reference [3], this formulation is extended so, that the right Cauchy-Green tensor of the anisotropic strain energy function is also approximated independently. In this presentation, we also approximate the cofactor and the volumetric dilatation of the anisotropic right Cauchy-Green tensor independently. We analyse the spatial convergence of the new mixed finite elements for hexahedral elements up to a cubic approximation in space. Thereby, we look especially at the different possible combinations of polynomial degrees of the independent mixed variables and the impact of this on the efficiency of the simulation (see Reference [5]). As numerical examples serve the well-known cooks cantilever beam and an axisymmetric pipe. Hereby, the bodies have different materials domains with different material parameters and fiber directions.
Abstract
Our research activity takes place within the research project GR 3297/4, funded by `Deutsche Forschungsgemeinschaft' (DFG), and aims at a robust simulation method for fiber-reinforced [...]
- 28
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A Practical Approach to Ontology-Based Data Modelling for Semantic Interoperability
T. Hagelien, H. Preisig, J. Friis, P. Klein, N. Konchakova

WCCM-ECCOMAS2020.

Abstract
Efforts to provide a standard representational framework based on current materials modelling and characterization knowledge facilitating collaboration, digital data representation, knowledge systems and semantic interoperability has been the main agenda for the European Materials Modelling Council (EMMC). One challenge in adopting the technology is related to the on-boarding process, particularly regarding the availability of ontologies and practical aspects to linking data to the ontologies, which requires deep insights in the current knowledge organization system. Latter challenges we address by constructing an interoperability framework based on data-models and explicit ontological mappings. Data models allow for building a representation of a computer system from different perspectives. The conceptual view identifies what real-world concepts the data represents. The logical perspective defines the rules and structures of how to implement the strategy. The physical perspective establishes the relationship between the data model and a specific database system. We show the ontology-based data modelling approach. It addresses the separation of the logical and the conceptual perspective, and allows for the development of the data-models. This approach also puts the data-models directly into production before applying the ontological mappings or developing the domain ontologies. Finally, we show a framework for information exchange that connects data models to physical storage and allows software applications to eliminate the need to support specific input-output operations, file conversion, file versioning, etc.
Abstract
Efforts to provide a standard representational framework based on current materials modelling and characterization knowledge facilitating collaboration, digital data representation, [...]
- 272
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Newton-Multigrid FEM Solver for the Simulation of Quasi-Newtonian Modeling of Thixotropic Flows
A. Ouazzi, N. Begum, S. Turek

WCCM-ECCOMAS2020.

Abstract
This paper is concerned with the application of Finite Element Methods (FEM) and NewtonMultigrid solvers to simulate thixotropic flows using quasi-Newtonian modeling. The thixotropy phenomena are introduced to yield stress material by taking into consideration the internal material microstructure using a structure parameter. Firstly, the viscoplastic stress is modified to include the thixotropy throughout the structure parameter. Secondly, an evolution equation for the structure parameter is introduced to induce the time-dependent process of competition between the destruction (breakdown) and the construction (buildup) inhabited in the material. This is done simply by introducing a structure-parameter-dependent viscosity into the rheological model for yield stress material. The nonlinearity, related to the dependency of the diffusive term on the material parameters, is treated with generalized Newton's method w.r.t. the Jacobian's singularities having a global convergence property. The linearized systems inside the outer Newton loops are solved using the geometrical multigrid with a Vanka-like linear smoother taking into account a stable FEM approximation pair for velocity and pressure with discontinuous pressure and biquadratic velocity spaces. We analyze the application of using the quasi-Newtonian modeling approach for thixotropic flows, and the accuracy, robustness and efficiency of the Newton-Multigrid FEM solver throughout the solution of the thixotropic flows using manufactured solutions in a channel and the prototypical configuration of thixotropic flows in Couette device.
Abstract
This paper is concerned with the application of Finite Element Methods (FEM) and NewtonMultigrid solvers to simulate thixotropic flows using quasi-Newtonian modeling. The [...]
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GMSH-FEM: An Efficient Finite Element Library Based on GMSH
A. Royer, E. Béchet, C. Geuzaine

WCCM-ECCOMAS2020.

Abstract
GmshFem is an open source C++ finite element library based on the application programming interface of Gmsh. Both share the same design philosophy: to be fast, light and user-friendly. This paper presents the main principles of GmshFem, as well as some scalability results for high-order scalar and vector finite element assembly on multi-core architectures.
Abstract
GmshFem is an open source C++ finite element library based on the application programming interface of Gmsh. Both share the same design philosophy: to be fast, light and user-friendly. [...]
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Bird Strike Virtual Testing Simulations and Results, for Preliminary Airframe Design Structural Optimization
P. Perdikoulis, E. Theotokoglou, I. Giannopoulos

WCCM-ECCOMAS2020.

Abstract
External airframe structural components facing the aircraft flight direction, are prone to bird collisions. Aircraft manufacturers meet the bird strike airworthiness requirements through physical bird strike testing. Mainly due to the high costs involved in the certification process, recent studies have highlighted the capabilities and benefits of hybrid simulationexperiment techniques that reduce certification costs. The numerical investigation presented herein, studied the bird-strike simulation methodologies implemented to support airframe manufacturers to partially fulfill the current certification airworthiness requirements. The methodology can be also applied during preliminary aircraft parametric design stages. In the current study, the method was applied onto an aircraft wing leading edge preliminary design, which led to design exploration by correlating the leading edge skin materials and thicknesses with the rib pitch positioning. The bird-strike impact model was simulated using the Smoothed Particle Hydrodynamics numerical method using ABAQUS® Explicit finite element package. The materials benchmarked were aluminum alloy 2024-T3, carbon fiber reinforced epoxy IM7/8552 and S2 glass Fiber Metal Laminate GLARE®. The design goal of the case study was to provide with preliminary evidence for impact resistance, quantified as residual permanent structural deformation of the critical structural components for which design charts were drawn and presented herein.
Abstract
External airframe structural components facing the aircraft flight direction, are prone to bird collisions. Aircraft manufacturers meet the bird strike airworthiness requirements [...]
- 25
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Reynolds Stress Model Adjustments for Separated Flows
A. Troshin, I. Matyash, S. Mikhaylov

WCCM-ECCOMAS2020.

Abstract
The development of a new Reynolds stress model suitable for computations of separated flows is described. It is based on the recently published version of SSG/LRRmodel, which includes a correction eliminating streamline back-bending near the reattachment point. Modifications are proposed which reduce the turbulence kinetic energy dissipation rate and pressure-strain term near the separation point. The validation results using the Diverging channel flow test case are presented. The quality of the obtained results is assessed.
Abstract
The development of a new Reynolds stress model suitable for computations of separated flows is described. It is based on the recently published version of SSG/LRRmodel, which [...]
- 22
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Numerical Prediction of a Large Bubble Behavior in Wall Turbulent Flow
N. Oshima, S. Kim

WCCM-ECCOMAS2020.

Abstract
Air lubrication systems for underwater applications have gained great popularity in recent years. Large bubbles, around We ≥ 100, show a large area of drag reduction than a small and microbubble, especially for large scale flow problems such as ship surface. However, it is hard to maintain their shape and prone to deform in a turbulent flow. In order to understand and control the drag reduction mechanism by the large bubble injection, it is necessary to know the behavior of large bubbles in the turbulent boundary layer and their interaction with the skin friction. In this study, a solver “interIsoFoam” for two-phase flow of an open-license software “OpenFOAM” is applied for an LES of turbulent channel flow with a large bubble, the gas-liquid interface of which is directly captured by improved VOF method. In a recent publication [1], we presented the numerical procedure of how to inject the large bubble on turbulent channel flow. The research objectives in this study are investigation on flow change of the horizontal channel flow included large bubble. From this observation, understanding large bubbles characteristic such as the surrounding flow phenomena was observed.
Abstract
Air lubrication systems for underwater applications have gained great popularity in recent years. Large bubbles, around We ≥ 100, show a large area of drag reduction than [...]
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Reverse Engineering and Process Modeling of Geometrically Complex Stiffened Shell Structures
C. Wolff, J. Batoz, A. Delamezière, E. Antaluca

WCCM-ECCOMAS2020.

Abstract
Thin-walled stiffened shell structures are very common as industrial products and their analyses by the finite element method can be difficult, in particular when the part is geometrically complex as found in the field of packaging. When the initial CAD definition is not available, reverse engineering is necessary, often based on the use of 3D scanners, in order to obtain a performing 3D geometrical model before considering finite element computations. The process of data capture to FEM can be time consuming and difficult for parts with several 3D stiffeners, depending on the strategies to reconstruct the part. This work focuses on the evaluation of three strategies applied to quite simple thin-walled parts using Geomagic and Abaqus software for the reconstruction and the simulation, respectively. Regarding FE simulations we focus on the computations of the first free frequency since this situation offers interesting comparison with experimental results. The criteria for the evaluation of the strategy are the times for scanning and processing of the data, the reconstruction, of the geometry for the FEM computations. We also study the influence of the strategies on the results of the simulations. These results depend on the type of element used and the present study reveals that for certain strategies the choice is restricted to the use of solid (mainly tetrahedron) elements, while another strategy allows the use of shell or solidshell elements. In this that case only one element through the thickness is used leading to very acceptable results for reduced calculation times but for a longer backward reconstruction time. The advantages and drawbacks of the 3D geometry reconstruction combined with FEM computational strategies are discussed.
Abstract
Thin-walled stiffened shell structures are very common as industrial products and their analyses by the finite element method can be difficult, in particular when the part [...]
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The Contribution of Vegetation to the Shallow Slopes Stability
P. Capilleri, S. Stacul, D. Presti

WCCM-ECCOMAS2020.

Abstract
Geometry is one of the main factors controlling the overall stability of levees, in addition to their hydraulic and mechanical characteristics, while in turn, their material strength strongly depends on their degree of saturation. Given that levees are usually partially saturated (Lo Presti et al., 2020) and that this partial saturation greatly contributes to their stability, any technique aimed at maintaining the levee in this condition is extremely useful. Protection of the levee sides by means of geogrids and biomats reduces the amount of infiltration by water, helps water adsorption by grass vegetation and contributes to mechanical strength thanks to the root apparatus of the grass cover. Vegetation is a good system for controlling slope erosion and instability. It can reduce the meteoric water that infiltrates into the soil and consequently the pore pressure. On the other hand, the root systems not only keep the soil partially saturated but also increase the soil shear strength with their mechanical contribution. The mechanical parameters of the root-soil system are important to evaluate the increase in soil shear strength due to the roots. Mechanically, roots contribute to the stabilization/reinforcement of soil by means of an additional apparent cohesion. It is believed that this apparent cohesion originates mainly from the root tensile strength, as well as capillary forces in partially saturated soils. In terms of root cohesion, an evaluation of this reinforcement can be obtained by means of direct shear tests. The authors set up a systematic experimental activity using a large direct shear box (Vannucci et al. 2019) with the purpose of considering the dual effect of suction and the soil tensile strength. A series of direct shear tests (large and standard shear box) were carried out. This paper presents the results of an experimental laboratory investigation on samples of rooted soil. In particular, the results of direct shear tests with a large shear box (300 × 300 × 100 mm) and with a standard shear box are shown. The results confirm an increase in the soil shear strength, in terms of cohesion, when roots are present. 1
Abstract
Geometry is one of the main factors controlling the overall stability of levees, in addition to their hydraulic and mechanical characteristics, while in turn, their material [...]
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Comparison of Different Quasi-Newton Techniques for Coupling of Black Box Solvers
N. Delaissé, T. Demeester, D. Fauconnier, J. Degroote

WCCM-ECCOMAS2020.

Abstract
Fluid-structure interaction (FSI) problems are frequently solved using partitioned simulation techniques with black-box solvers, reusing reliable and optimized codes. These problems can principally be reduced to solving a root-finding problem. In case of strong coupling, pure Gauss-Seidel iterations between the structure and flow solvers are unstable for lower modes. In these cases, quasi-Newton techniques are used, which construct an approximation of the Jacobian or its inverse by reusing information from previous iterations and time steps. Four different quasi-Newton techniques are compared: the interface quasi-Newton algorithm with an approximation for the inverse of the Jacobian from a least-squares model(IQN-ILS), the interface block quasi-Newton algorithm with approximate Jacobians from least-squares models(IBQN-LS), the interface quasi-Newton technique with multiple vector Jacobian(IQN-MVJ) and the multi-vector update quasi-Newton technique(MVQN). These coupling algorithms are differentiated based on whether the approximation of the Jacobian is performed for the entire black-box system (IQN-ILS and IQN-MVJ) or for both individual solvers (IBQN-LS and MVQN). Moreover, a distinction is made between methods which perform the approximation with either least-squares models (IQN-ILS and IBQN-LS) or multivector techniques (IQN-MVJ and MVQN). Their performance is compared by solving a 1D flexible tube case, using the in-house coupling software CoCoNuT. Both the memory usage and number of iterations between structure and flow solvers in each time step are examined. The techniques using a multi-vector approach require explicit matrix construction, so that memory requirements scale quadratically, whereas the least-squares techniques have a matrix-free implementation, resulting in linear scaling. In terms of convergence they are comparable.
Abstract
Fluid-structure interaction (FSI) problems are frequently solved using partitioned simulation techniques with black-box solvers, reusing reliable and optimized codes. These [...]
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Effect of Climatic Actions On Buildings with Internal Insulation and Thermal Breaks: Multi-Scale Approach and Thermo-Hydro-Mechanical Modeling
T. Meng, H. Somja, F. Meftah, P. Heng

WCCM-ECCOMAS2020.

Abstract
For buildings designed with internal insulation, thermal bridges at the junction between slabs and walls are a common issue, since they create heat loss from inside of the building. Thermal break systems (TBS), which are composed of structural elements (rebars and steel profiles) and insulation material, are used to reduce this heat loss and to transfer shear forces from the slab to the walls. Insulation system of TBS generates a temperature gap from wall to slab. As a consequence, while the wall is exposed to climatic actions and is repeatedly dilated and contracted, whereas the slab pertains a constant temperature and does not present any volumetric variation, thus the TBSs are submitted to large displacement constrains. The paper illustrates the effect of the thermal dilatation and contraction of the walls, which create a supplemental force in the TBSs, and consequently cracking of the walls. A numerical model of a quarter of a building's storey is submitted to the climatic actions computed at the location of Embrun city, in France. One side of the L-shape wall is supposed to face to the south, and the other one to the west. The thermal and mechanical analysis are performed with the software CASTEM. In thermal analysis, air temperature and flux of solar radiation signal are defined from databases of METEO FRANCE, and are applied on the exterior surface of the walls. The results of the first calculation, by thermo-hydro-mechanical analysis (THM) with elasticity behavior, confirm that a significant stress level in tension occurs in the concrete at the corner of the walls and the nearby interface elements of the TBS. Furthermore, the TBSs that are close to the corner of the walls pertain the highest horizontal and axial forces, and are at risk to exceed the limit strength. Based on those results, a second calculation, which includes the coupling of damage with shrinkage and creep model from the THM analysis, is made for determining more realistic forces in the TBSs, and analyzing the cracking pattern of the walls.
Abstract
For buildings designed with internal insulation, thermal bridges at the junction between slabs and walls are a common issue, since they create heat loss from inside of the [...]
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A Semi-Analytical Isogeometric Analysis of Leaky Wave Propagation in 3D Waveguides Coupled with Fluids
F. Seyfaddini, H. Nguyen-Xuan, V. Nguyen

WCCM-ECCOMAS2020.

Abstract
Guided waves are widely used as a non-destructive technique for the detection of defects or damage in structures due to the their excellent propagation characteristics. Developing an efficient calculation of guided waves is crucial in this context. In this work we present an approach named semi-analytical isogeometric analysis (SAIGA) for computation of dispersion properties of fluid-coupled waveguides in three-dimensional structures. The proposed approach is based on the use of Non-Uniform Rational B-splines (NURBS) as the basis functions for the geometry representation and for solution's approximation. It is shown that the using NURBS basis functions has significant advantage over using Lagrange basis functions for computing the dispersion of leaky waves in immersed waveguides due to their higher smoothness feature.
Abstract
Guided waves are widely used as a non-destructive technique for the detection of defects or damage in structures due to the their excellent propagation characteristics. Developing [...]
- 30
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Numerical Simulation of Flow in a Fuel-Injector of an Aircraft Engine Combustor Using Building-Cube Method
Y. Cho, R. Bale, M. Tsubokura, N. Oshima

WCCM-ECCOMAS2020.

Abstract
In this study, we investigate grid dependency on local mesh refinement for the numerical simulation of cold flow in an aircraft engine's fuel-injector. The numerical simulation of fully compressible Navier-Stokes equations is conducted using a hierarchical Cartesian mesh-based solver known as 'CUBE'. Using the results of the high-resolution simulation as the basis, the gird dependency analysis is carried out. In addition, we evaluate the weak scaling of the underlying solver.
Abstract
In this study, we investigate grid dependency on local mesh refinement for the numerical simulation of cold flow in an aircraft engine's fuel-injector. The numerical simulation [...]
- 58
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Comparative Analysis of Bracing Systems in a Steel Structure Shed
N. Anunciação, L. Souza, A. Pereira, C. Ribeiro, M. Barboza

WCCM-ECCOMAS2020.

Abstract
The sheds, usually in metal structure, are commonly used for commercial or industrial establishments. Such structures can be designed under the laws established by the Ultimate Limit State (ULS) parameters, Service Limit Status (SLS) or Usage (SLU), even though many of them may be subject to large displacements caused by vibrations, static loads or, even the combination between both. The own weight's structure and the wind dynamic load combined is a perfect example how these structures are subjected to combined forces. Thus, alternatives to control or minimize the excessive displacement are needed. There are several methods of controlling vibration, and this paper presents the bracing system. Shed and 3 different bracing systems were designed, single diagonal, double diagonal and inverted V. These systems are designed to resist vertical and horizontal actions, and its main function is to provide stability to structures when they suffer from wind load action. In this paper NBR 6123/1988 was used to compute wind load. Numerical calculations were carried out in SAP2000 and Visual Ventos, in order to study the dynamic behaviour of the shed submitted to such actions. The analyses were restricted only to displacements in the X and Y directions. Afterwards, the reinforced structure was compared with that one without bracing. After the computations the minimal X and Y displacement were found for inverted V-shaped bracing system. Furthermore, the reinforce structure also provided great rigidity to the frame and a better distribution of the efforts in the structure nodes.
Abstract
The sheds, usually in metal structure, are commonly used for commercial or industrial establishments. Such structures can be designed under the laws established by the Ultimate [...]
- 29
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Global Local Analysis with Robin Parameters: Applications to Crack Propagation in 2D and 3D Models
I. Fuenzalida-Henriquez, E. Castillo-Ibarra, J. Hinojosa

WCCM-ECCOMAS2020.

Abstract
Global local analysis is a part of the structural analysis that allows to study, with an iterative solution, a coarse global linear model with a specific zone. This zone is defined as a local model with fine mesh and a non-linear behaviour such as crack propagation. However, the current trend in Global Local analysis is to impose displacements on the fine model to later obtain the reactions that will be applied to the global model for each iteration (Primal to Dual solution algorithm). Therefore, we propose a mixed analysis in the local and global models through the application of Robin conditions on the interface, allowing a higher grade of flexibility for the case of the patch or fine model with crack propagation behaviour. As a result, the algorithm converges successfully, presenting kinematic compatibility and good results with respect to the Monolithic (non-decomposed) model. Finally, a sensitivity analysis is performed on some variables regarding the crack propagation for 2D models. Finally, the proposed methodology also allows to improve the performance of the method for cracked models or other nonlinearities when compared with the current global local analysis, presented in the state of the art.
Abstract
Global local analysis is a part of the structural analysis that allows to study, with an iterative solution, a coarse global linear model with a specific zone. This zone is [...]
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Volume of Fliuds Interface Reconstruction with Curvature and Corner Definitions
J. Yao, J. Liu

WCCM-ECCOMAS2020.

Abstract
Interface reconstruction with VOF (volume of fluids) is an essential phase in an ALE (Arbitrary Lagrange & Eulerian) simulation. Some historical issues associated with the Youngs method have not been well addressed. One is that the slope estimate is not always accurate. A more serious issue is that the interface is discontinuous on cell faces with a curved interface geometry. Plus, with an existing VOF method a corner cannot be reconstructed in general. We propose a new VOF approach in order to address these issues. We treat the case of a single material and void, and the partial volumes in mixed cells exactly given. We assume the nodes not owned by any pure elements are sparsely distributed in a mesh. This is generally true for a moderate curvature. Then, most mixed cell nodes can be coloured with pure elements, and can provide orientation of interface facets. For a given interior mixed zone in two-dimensions, we find its mixed neighbours and three partial volumes are given. A linear facet has two degrees of freedom therefore can be reconstructed with a local optimization with volume matching. A quadratic facet (with three degrees of freedom) can be computed exactly that matches the known partial volumes. This is to say a planar interface geometry can be locally exactly reconstructed away from a corner, and interface curvature can be calculated with neighbour volume fractions. The case of a corner can be identified with a sudden slope change and high curvature with noticeable gaps between neighbour facets. Then, a local optimization for matching volumes can again be performed and the corner is reconstructed. We have implemented this algorithm in 2D at the Lawrence Livermore National Laboratory. Preliminary tests show that exact planar geometries can be reconstructed, and corners can be accurately defined. In the case of a curved geometry, the gaps between neighbour facets are of high order. When necessary, the gaps between facets can be eliminated by a local modification of a facet without affecting the order of accuracy. The proposed algorithm is by nature applicable to an arbitrarily given mesh because the only necessary requirement is a function to accurately compute the partial volume bounded by a facet (linear, corner, circular, or conic). A similar approach is expected to work in 3D provided an accurate method to compute volumes.
Abstract
Interface reconstruction with VOF (volume of fluids) is an essential phase in an ALE (Arbitrary Lagrange & Eulerian) simulation. Some historical issues associated with [...]
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Predicting Mud Motor Performance and Reliability with Reduced Order Modeling
A. Kolyshkin

WCCM-ECCOMAS2020.

Abstract
In this paper we present a reduced order model for simulating mud motor performance and reliability. The model breaks down a mud motor power section to a set of 2D simulations with simplified drilling fluid flow description. It can reliably predict power curves and failure risks caused by elastomer fatigue, hysteresis heating, and debonding. The model can capture mud compatibility effects as well.
Abstract
In this paper we present a reduced order model for simulating mud motor performance and reliability. The model breaks down a mud motor power section to a set of 2D simulations [...]
- 90
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High-Order Flux Reconstruction Based on Immersed Boundary Method
J. Kou, S. Joshi, A. Hurtado-de-Mendoza, K. Puri, C. Hirsch, E. Ferrer

WCCM-ECCOMAS2020.

Abstract
In the last decade, high-order methods for Computational Fluid Dynamics (CFD) are becoming attractive for unsteady scale-resolving-simulations in industrial CFD applications, due to their advantages of low numerical dissipation, high efficiency on modern architectures and quasi mesh-independence. However, the generation of body-fitted mesh for high-order methods is still a significant bottleneck and often determines the overall quality of the solution. To avoid the complexity of mesh generation, the present work combines the numerical advantages of the high-order Flux Reconstruction (FR) method and the simplicity of the mesh generation based on Immersed Boundary Method (IBM) that allows solving flow past obstacles on a non body-fitted mesh. The volume penalization method is selected for its ease of implementation and robustness. The proposed method is validated by several test cases, including flow past a cylinder and NACA0012 airfoil for static and moving boundaries. Good agreement with body-fitted simulation is reported.
Abstract
In the last decade, high-order methods for Computational Fluid Dynamics (CFD) are becoming attractive for unsteady scale-resolving-simulations in industrial CFD applications, [...]
- 94
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Simulation of the Fluid-Structure Interaction Involving Two-Phase Flow and Hexagonal Structures in a Nuclear Reactor Core
S. Houbar, A. Gerschenfeld, G. Allaire

WCCM-ECCOMAS2020.

Abstract
In order to enhance safety assessments of Sodium Fast Reactors (SFR), some scenarios involving transient Fluid-Structure Interactions (FSI) are investigated using numerical simulation tools. SFRs are indeed quite sensible to mechanical deformations regarding their nuclear power (see [1] for more details). The originality of the scenario presented in the paper is to consider sufficient large mechanical interactions involving a large pressure decrease in the fluid domain. This decrease leads to vaporization of the fluid and then to a different impact on the structures. By means of the open-source software Code Saturne developed by EDF [2], this scenario is investigated in 2D using a 3-equation model derived from the Navier-Stokes equations while an harmonic model is applied for the mechanical structures. The code coupling is managed using the Newmark algorithm for the mechanical part and a damped fixed point algorithm in order to get a converged coupled FSI problem.
Abstract
In order to enhance safety assessments of Sodium Fast Reactors (SFR), some scenarios involving transient Fluid-Structure Interactions (FSI) are investigated using numerical [...]
- 30
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Numerical Study of the Interaction Between Focused Ultrasound Wave and Brain-Like Soft Material
Z. Du, Z. Liu

WCCM-ECCOMAS2020.

Abstract
Focused ultrasound is of great significance in the fields of medical ultrasound imaging, diagnosis, and treatment, yet little is known about the quantification of the physical effects of focused ultrasound and the analysis of the corresponding biological effects. In this paper, the acoustic-solid-thermal coupled computational model is developed to study the interaction between focused ultrasound and brain-like soft materials. Firstly, a hyperviscoelastic constitutive model is established to describe the dynamic and thermal-mechanical behaviour of brain-like soft material. Due to the high compression resistance and low shear resistance of brain-like soft materials, it will appear in the focus area that Compression strain and shear strain are approximate, but compressive stress is much larger than shear stress. Secondly, the dynamic mechanical response of brain-like soft materials under focused ultrasound excitation with different frequencies and amplitudes were studied. By analyzing the hysteresis loop of the feature points in the focus area, it can be concluded that the loss angle of dynamic modulus of brain-like soft materials increases with the increase of load frequency and the increase of load frequency. The higher the load amplitude is, the greater the energy input to the focusing region is, and the faster the dissipation speed is. At last, through the multi-field coupled simulation, it is found that the focusing accuracy of the focused ultrasound increases with the increase of the frequency, but the focusing energy intensity will decrease. The input energy has an optimized value in a specific frequency range. The research is helpful for the improvement of focused ultrasound diagnosis, imaging and treatment technology, and the use of dynamic mechanical property inversion of brain-like soft materials.
Abstract
Focused ultrasound is of great significance in the fields of medical ultrasound imaging, diagnosis, and treatment, yet little is known about the quantification of the physical [...]
- 15
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Interface Sharpening in Two-Phase Flows Based on Primitive Sub-Cell Reconstructions
I. Menshov, C. Zhang, P. Zakharov

WCCM-ECCOMAS2020.

Abstract
The paper addresses a novel interface-capturing approach for two-phase flows governed by the five-equation diffuse interface model. To suppress the numerical diffusion of the interface, we introduce a primitive sub-cell reconstruction based on volume fractions in neighbouring cells. This reconstruction gives rise to a Riemann problem (CRP) with an additional contact discontinuity, so-called composite Riemann problem, which is stated on mixed cell faces. The CRP solution is used to calculate the numerical flux across cell faces of mixed cells with taking into account the interface reconstructed patterns. A hybrid HLLHLLC method is incorporated to approximate the solution of the CRP. The proposed approach is shown to effectively reduce the interface numerical diffusion without introducing spurious oscillations. Its performance and robustness is examined by 1D and 2D numerical tests.
Abstract
The paper addresses a novel interface-capturing approach for two-phase flows governed by the five-equation diffuse interface model. To suppress the numerical diffusion of [...]
- 27
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Applications of a Nodal-Integration-Based Finite Element Method to Non-Linearc Problems
Y. JIA, J. LEBLOND, J. ROUX, R. Lacroix, J. Bergheau

WCCM-ECCOMAS2020.

Abstract
In this paper, we firstly introduce a nodal-integration-based finite element method. The method allows the use of first-order tetrahedral elements without suffering from the volumetric locking problem. The most important advantage of tetrahedral meshes is that they can be automatically generated for complex geometries using existing reliable meshing tools. The method is then applied to 3 types of applications. The first application is a large displacement, large strains elastic-plastic simulation on a notched specimen. The second application is an elastic-plastic bending problem. And the last example concerns the numerical simulation of the thermo-mechanical problem. In all the cases, the solution given by the nodal-integration-based FEM is compared to more classical FEM results.
Abstract
In this paper, we firstly introduce a nodal-integration-based finite element method. The method allows the use of first-order tetrahedral elements without suffering from the [...]
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Simulation of Guided Waves in Cylinders Subject to Arbitrary Boundary Conditions Using the Scaled Boundary Finite Element Method
D. Itner, H. Gravenkamp, D. Dreiling, N. Feldmann, B. Henning

WCCM-ECCOMAS2020.

Abstract
The scaled boundary finite element method (SBFEM) excels as a tool for numerical analysis at particular problem setups where the analytical solution in the scaling direction can be exploited to improve computational efficiency by reducing the number of required degrees of freedom (DOF). This is especially the case for simulating axisymmetric waveguides in the high-frequency range, allowing a significant decrease of computational costs (both memory and CPU time). Then, only the radial direction in a cylindrical coordinate system is discretized and the axial direction is solved analytically. A full threedimensional formulation is possible via the Fourier transform to include asymmetries. This contribution presents such an axisymmetric formulation, which is extended to allow the definition of circumferential as well as arbitrarily shaped dynamic boundary conditions (BCs). Furthermore, the required number of DOF depends on the frequency content. Hierarchical shape functions allow to dynamically adapt the DOF, further increasing efficiency. It will be shown that the results are in good agreement with standard finite element procedures, while greatly reducing computational time.
Abstract
The scaled boundary finite element method (SBFEM) excels as a tool for numerical analysis at particular problem setups where the analytical solution in the scaling direction [...]
- 20
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Advanced Numerical Models for Design and Optimization of Thrust Bearing Hydrodynamic Characteristics
A. Olga, Y. Boldyrev, A. Borovkov, I. Voynov

WCCM-ECCOMAS2020.

Abstract
Efficiency of hydrodynamic thrust bearings used in a wide range of power machines is characterized by including the load capacity of an oil wedge, which has nonlinear dependence on gap size. In this study we consider the different types of lubricant layer microgeometry profiling with the aim of optimal design of the hydrodynamic bearing characteristics for ensuring the maximum load capacity using advanced numerical models and methods. We enlarge the results of significant research works of J.W. Rayleigh and S. Y. Maday in relation to the hydrodynamic sector self-aligning acting thrust bearings based on advanced numerical methods. Different geometrical parameters which define profile curvature were used as optimization variables. The maximum of pressure integral over the lubricant layer surface as objective function was used. Hydrodynamic problems using Navier-Stocks equations were solved based on numerical approach and commercial CFD code ANSYS/CFX using the St.Petersburg Polytechnic Supercomputer Center.
Abstract
Efficiency of hydrodynamic thrust bearings used in a wide range of power machines is characterized by including the load capacity of an oil wedge, which has nonlinear dependence [...]
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HP-Multigrid for RANS-Modeled Turbulent Flows in a High-Order Flux Reconstruction Framework
S. Joshi, A. Hurtado-de-Mendoza, J. Kou, K. Puri, C. Hirsch, E. Ferrer

WCCM-ECCOMAS2020.

Abstract
High-order (HO) methods are of concerted academic and industrial interest in recent years due to their improved accuracy and their capability to deal with complex geometries [1]. Of particular note is the flux reconstruction method [2], which unifies several existing HO schemes into a simpler and computationally efficient approach that has been shown to work on all element types (including simplices) in two and three dimensions. There is considerable interest to apply HO methods to industrially relevant problems. At the same time, accurate and robust turbulence modeling techniques are essential for reliable results. As outlined in the National Aeronautics and Space Administration's CFD vision 2030 study, Large Eddy Simulation (LES) still remains impractical for industrial cases therefore, Reynolds-Averaged Navier Stokes (RANS) and hybrid RANS-LES methods hold high significance in the near future [4]. Achieving fastest convergence to steady-state is important in the context of RANS simulations, for which several convergence acceleration techniques are being investigated. Multigrid methods are an industry standard in Finite Volume (FV) type schemes and are increasingly being applied to HO methods in the form of p-multigrid [22]. They exploit the polynomial hierarchy of the solution space to represent errors on a coarser resolution. A natural extension of this idea is hp-multigrid, where we can augument the classical h-multigrid to the polynomial hierarchy [23]. In this paper we illustrate the application of high-order flux reconstruction methods to simulate compressible, turbulent flows on body-fitted meshes. The case in point is the turbulent flow over a flat plate [24]. Turbulence is modeled through the RANS approach using the one-equation Spalart-Allmaras model. Grid-coarsening for the h-levels is performed by removing every other line in each direction from the original mesh. The system is driven to a steady-state solution using hp-multigrid convergence acceleration with local time-stepping using an explicit Runge-Kutta time-marcher. We show that the augumented h-multigrid is highly effective with a 10X to 24X drop in convergence time.
Abstract
High-order (HO) methods are of concerted academic and industrial interest in recent years due to their improved accuracy and their capability to deal with complex geometries [...]
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Construction of Programming Education Environment Using Problem Solving Environment
S. Hioki

WCCM-ECCOMAS2020.

Abstract
There are many problems in the research and educational field. Japanese PSE has started in the research area: DEQSOL and NCAS. In Japanese elementary school, programming education will begin this year. After that, the programming education in junior high school and high school are also planned. Thus, the need for programming education is highly expected recently. However, it seems not satisfactory when it comes to self-study environment. In this article, construction of the educational platform ( internet sites ) for the programming beginners will be introduced. This sites includes three programming languages to learn: scratch, C++ and python. Users ( learners ) meets the question first, then answer this question in terms of their programming code. Efficiency in the university class is briefly discussed.
Abstract
There are many problems in the research and educational field. Japanese PSE has started in the research area: DEQSOL and NCAS. In Japanese elementary school, programming education [...]
- 23
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Sensitivity Analysis for Model with Dependent Inputs Using Sparse Polynomial Chaos Expansions
D. Xiao, M. Ferlauto, L. Song, J. Li

WCCM-ECCOMAS2020.

Abstract
Polynomial chaos expansions (PCE) meta-model has been wildly used and investigated in the last decades in sensitivity analysis (SA), which adopts a variety of orthogonal polynomials to approximate the system response and calculates sensitivity indices directly from the polynomial coefficients. The Sobol' index is one of prevalent sensitivity indices for model with independent inputs and can be easily obtained after constructing generalized polynomial chaos (gPC). But for dependent inputs, a typical approach is based on the procedure of transforming the dependent inputs into independent inputs according to the literature. This paper demonstrates a global sensitivity analysis (GSA) approach for dependent inputs, in which Gram-Schmidt orthogonalization (GSO) numerically computes the orthonormal polynomials for PCE. The especial procedure for dependent inputs to obtain sensitivity indices lies in the linearly independent polynomials basis for GSO must be in an intended order. Besides, to alleviate the curse of dimensionality, the sparse polynomial chaos (sPC) is built coupling with least angle regression (LAR) and a nested experimental design called weighted Leja sequences (wLS). Then cross validation (CV) determines the best truncated set for sPC with the suitable size of experimental design in use. In the end, this proposed approach is validated on a benchmark function with dependent inputs. The results reveal that the proposed approach performs well to calculate sensitivity indices for model with dependent inputs.
Abstract
Polynomial chaos expansions (PCE) meta-model has been wildly used and investigated in the last decades in sensitivity analysis (SA), which adopts a variety of orthogonal polynomials [...]
- 27
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Coupled Adjoint Fluid-Structure Interaction Technique for Flexible Wing Shape Optimization
K. Tsiakas, G. Roge, X. Trompoukis, V. Asouti, G. Fougeron, S. Julisson, L. Martin, S. Kleinveld, K. GIannakoglou

WCCM-ECCOMAS2020.

Abstract
This paper presents the Multi-Disciplinary Optimization (MDO) of a business jet including static aeroelastic effects. Two different CFD tools (AETHER by Dassault Aviation and PUMA by NTUA) are coupled with a CSM model (VPS software by ESI). Single discipline as well as coupled multi-disciplinary sensitivity derivatives (SDs) are computed by means of adjoint methods. Both a purely discrete and a hybrid continuous(fluid)/discrete(structure) adjoint formulations are presented. The computed SDs are verified against finite differences.
Abstract
This paper presents the Multi-Disciplinary Optimization (MDO) of a business jet including static aeroelastic effects. Two different CFD tools (AETHER by Dassault Aviation [...]
- 50
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Numerical Boundary Conditions for Schemes with Centered and Biased Differences in Subsonic Gas Dynamics
I. Abalakin, L. Dorodnicyn

WCCM-ECCOMAS2020.

Abstract
For finite-difference schemes of EBR class in multi-dimensional inviscid gas dynamics, the nonreflecting boundary conditions are analyzed and developed. The wave-reflection properties of discrete models differ significantly from each other and from the continuous Euler equations. For certain schemes there exist local boundary conditions which lead to small reflections of waves with arbitrary incidence angle. Numerical examples are shown both linear and nonlinear.
Abstract
For finite-difference schemes of EBR class in multi-dimensional inviscid gas dynamics, the nonreflecting boundary conditions are analyzed and developed. The wave-reflection [...]
- 13
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Approximate Bayesian Computation Applied to Model Selection and Parameter Calibration in Cell Proliferation
N. Silva, B. Loiola, J. Costa, H. Orlande

WCCM-ECCOMAS2020.

Abstract
Approximate Bayesian Computation is used in this work for the selection and calibration of cell proliferation models. Four competing models based on ordinary differential equations are analyzed, by using the measurements of the proliferation of DU-145 prostate cancer viable cells during seven days. The selection criterion of the ABC algorithm is based on the Euclidean distance between the model prediction and the experimental observations. The Richards Model and the Generalized Logistic Model were selected by the ABC algorithm used in this work, providing accurate estimates of the evolution of the number of viable cells. Bayes factor revealed that there was no evidence in favor of any of these two selected models.
Abstract
Approximate Bayesian Computation is used in this work for the selection and calibration of cell proliferation models. Four competing models based on ordinary differential [...]
- 46
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Numerical Investigation of Model Fusiform Aneurysms: Influence of Maximum Diameter to Height Ratio
N. Philip, P. V, S. J.

WCCM-ECCOMAS2020.

Abstract
In the current clinical practice, the rupture risk prediction of fusiform aneurysms is based on maximum diameter. This approach does not account for the size and shape dependent cyclic stresses arising due to fluid-solid interaction (FSI). Previous fluid-structure interaction studies by the authors on model two dimensional fusiform aneurysms (abdominal aortic aneurysm (AAA)) has revealed that the maximum diameter to height ratio (DHr) could possibly be used as a critical parameter, since it can signify the hemodynamic and biomechanical stresses [7]. Hence the present study assesses whether the observations from the shape index based 2D simulations hold good in realistic 3D conditions as well. Based on the preliminary investigations, it is hypothesized, that a combination of Dmax and DHr would be a better indicator of rupture risk.
Abstract
In the current clinical practice, the rupture risk prediction of fusiform aneurysms is based on maximum diameter. This approach does not account for the size and shape dependent [...]
- 30
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CFD/CSD Coupling for an Isolated Rotor Using preCICE
Q. Huang, A. Abdelmoula, G. Chourdakis, J. Rauleder, B. Uekermann

WCCM-ECCOMAS2020.

Abstract
Modeling a rotor blade flow field involves computing the blade motion, elastic deformation, and the three-dimensional forces and moments for specific trim conditions. Such a complex multiphysics problem, which includes a strong fluid-structure interaction, should be modeled by coupling separate solvers which are specialized on solving single-physics problems. In this work, we present a modular and extensible TAU-CAMRAD II coupling environment using the preCICE coupling library [1]. In this coupling, the aerodynamic forces and moments were computed with the CFD solver TAU. The blade control angle for the CFD simulation were determined by the CSD solver CAMRAD II. We validated the implementation using a modified model of the HART-II rotor at an advancing ratio of µ=0.3. Besides the potential that this work unlocks for future simulations of an active rotor, it also serves as an example of using preCICE for geometric multi-scale (1D-3D) coupling of closed-source solvers for periodic phenomena.
Abstract
Modeling a rotor blade flow field involves computing the blade motion, elastic deformation, and the three-dimensional forces and moments for specific trim conditions. Such [...]
- 24
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Numerical Simulation of the Molten Pool of a Powder Bed
Y. SAADLAOUI, E. Feulvarch, J. LEBLOND, J. Bergheau

WCCM-ECCOMAS2020.

Abstract
In this study, a numerical approach is developed to simulate the molten pool formation during the melting of a powder bed. It is based on a fluid formulation that allows taking into account the dynamics in the molten pool through the two effects of surface tension (including both 'curvature effect' and the 'Marangoni effect') and buoyancy. Additionally, the free surface is considered using an ALE method. The shrinkage of the powder layer after its melting and the change of the thermo-physical properties depending on the material state (powder or compact) are also modeled. As an application, a 3D thermo-fluid simulation of the powder bed melting is carried out. It is found that the powder layer porosity has a great effect on the molten pool morphology.
Abstract
In this study, a numerical approach is developed to simulate the molten pool formation during the melting of a powder bed. It is based on a fluid formulation that allows taking [...]
- 34
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Concave Surface Base-Isolation System Against Seismic Pounding of Irregular Adjacent Buildings
F. Mazza, R. Labernarda

WCCM-ECCOMAS2020.

Abstract
The application of the concave surface sliders (CSSs) as seismic-isolation system of buildings is growing due to the automatic coincidence between the projection of the gravity mass centre of the superstructure and the stiffness centre of the CSSs, during the sliding phase, and self-re-centring properties, after an earthquake. These advantages make them attractive for the retrofitting of adjacent fixed-base framed buildings with irregular plan that may experience significant seismic pounding induced by torsional displacements. However, friction force and lateral stiffness of the CSSs present continuous variation during an earthquake because they are proportional to the axial load. Moreover, further changes of the friction force result from variation of the friction coefficient depending on the sliding velocity, with reduction at the onset of motion of the CSS and motion reversals, axial pressure and temperature at the sliding surface. In this work, structural pounding incidences are investigated with reference to five-storey reinforced concrete (r.c.) framed structures with an L-shaped plan placed adjacent to form Tand C-shaped plans. A simulated design of the original fixed-base buildings is preliminarily carried out in accordance to an old Italian code, for a medium-risk seismic zone and a typical subsoil class. Then, the seismic retrofitting of the residential buildings is carried out with the CSS bearings, for attaining performance levels imposed by current Italian code in a high-risk seismic zone and for moderately-soft subsoil. The design of the base-isolation systems is carried out on the assumption that the same radius of curvature is considered for all the isolators, with constant or variable dynamic-fast friction coefficients. A computer code for the nonlinear dynamic analysis of the fixed-base and base-isolated test structures is developed, in order to compare different models of the CSS bearings that consider constant and variable axial load combined with friction coefficient at breakaway and stick-slip and as function of the sliding velocity, axial pressure and temperature. The inelastic response of the superstructure is also taken into account by a lumped plasticity model at the end sections of r.c. frame members, where flat surface modelling of the axial load-biaxial bending moment elastic domain is adopted. Attention is focused on the pulse-type and non-pulse-type nature of near-fault earthquakes.
Abstract
The application of the concave surface sliders (CSSs) as seismic-isolation system of buildings is growing due to the automatic coincidence between the projection of the gravity [...]
- 26
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Seismic Demand of Masonry Infills in R.C. Structures Accounting for the In-Plane/Out-of-Plane Interaction
F. Mazza, A. Donnici

WCCM-ECCOMAS2020.

Abstract
The out-of-plane verification of unreinforced masonry infills (MIs) placed at different floor levels of a building is generally carried out through simplified methods, but seismic events in Italy (e.g. L'Aquila, 2009) and worldwide (e.g. Northridge, 1994) have highlighted that code provisions may result in wrong estimations of safety. The types of damage observed for MIs are usually a combination of, or an interaction between, in-plane (IP) and outof-plane (OOP) mechanisms. Specifically, the IP drift ratio is generally reduced at the upper storeys of buildings, where the OOP drift ratio increases due to an increase of seismic acceleration. Significant OOP damage may also take place at the lower storeys where the highest values of IP drift ratio are attained. The present work is aimed at identifying the effects of the IP and OOP nonlinear interaction of MIs on their seismic behaviour and acceleration demand. A five-element macro-model comprising four diagonal nonlinear beams and one (horizontal) central nonlinear truss for the prediction of the OOP and IP behaviour of MIs, respectively, is first implemented in a C++ computer code for the nonlinear dynamic analysis of r.c. infilled framed structures. The proposed algorithm addresses the issue of nonlinear interaction by modifying stiffness and strength values of the MI in the OOP direction on the basis of simultaneous or prior IP damage and vice versa. Moreover, a lumped plasticity model describes the inelastic behaviour of r.c. frame members, including a 26-flat surface modelling of the axial load-biaxial bending moment elastic domain at the end sections where inelastic deformations are expected. A spatial one-bay multi-storey shear-type model is considered as equivalent to infilled r.c. framed buildings. In particular, the dependence of the results on variation of the following design parameters is considered: i.e. number of storeys; bay length; aspect ratio of MIs, with two leaves of clay hollow bricks, defined as the ratio between the panel length and height; strength level of the r.c. framed structure. Biaxial spectrum-compatible accelerograms are considered at ultimate limit states. A review of the current Italian (NTC18), European (EC8) and American (FEMA356) code provisions is performed by means of comparison with analyses results.
Abstract
The out-of-plane verification of unreinforced masonry infills (MIs) placed at different floor levels of a building is generally carried out through simplified methods, but [...]
- 22
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Non-Prismatic Beam-Like Structures with 3D Cross-Sectional Warping
G. MIGLIACCIO

WCCM-ECCOMAS2020.

Abstract
Many complex engineering structures, e.g. blades of wind turbines and helicopters, are beamlike and non-prismatic. They may be tapered, twisted and curved in their unstressed state, undergo large displacements of the centre-line, and cross-sectional warping in and out of plane. For their structural modeling, an approach based on beam elements can be the best compromise between computational efficiency and accuracy, but classical beam models (see, for example, the monumental Love's treatise) may not be sufficient. Better results may be obtained by exploiting geometrically exact and asymptotic approaches. This paper proposes a physical-mathematical model for the aforementioned non-prismatic structures. Analytical results obtained for small warping and strain fields are presented and compared to the results obtainable from nonlinear 3D-FEM analyses.
Abstract
Many complex engineering structures, e.g. blades of wind turbines and helicopters, are beamlike and non-prismatic. They may be tapered, twisted and curved in their unstressed [...]
- 35
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Effect of Step Surface Imperfections on Boundary Layer Transition
Y. Lin, J. Wang

WCCM-ECCOMAS2020.

Abstract
Surface imperfections due to manufacturing tolerance, such as steps, gaps, and waviness, can cause early boundary layer transition, thus reduce the practicability of the natural laminar flow (NLF) technology for aircraft drag reduction. In this study, a new numerical methodology is proposed and implemented to predict the effect of backward-facing step (BFS) and forward-facing step (BFS) on boundary layer transition over NLF aircraft body. The method is based on a hypothesis that the effect of surface imperfections on boundary layer flow can be mimicked as that of surface roughness due to the relevant small size of the imperfection compared to the local boundary layer thickness. The predicted transition location on BFS/FFS surface agrees very well with the experimental validation data. It implies the applicability and capability of this approach for transition location prediction over more general surface imperfection arrangements. The study thus provides an efficient, practical prediction tool to determine the manufacturing allowance on surface imperfection dimension on NLF body for aerodynamic engineers.
Abstract
Surface imperfections due to manufacturing tolerance, such as steps, gaps, and waviness, can cause early boundary layer transition, thus reduce the practicability of the natural [...]
- 46
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Numerical Simulation of Shock Boundary Layer Interaction Using a Shock Fitting Technique
A. Assonitis, R. Paciorri, A. Bonfiglioli

WCCM-ECCOMAS2020.

Abstract
The unstructured shock-fitting algorithm originally proposed in Ref. [3] has been further developed to make it capable of dealing with shock-wave/boundary-layer interactions (SWBLIs). This paper illustrates the algorithmic features of the technique and its application to 2D flow-configurations featuring different SWBLIs, including the transonic turbulent flow past a symmetrical airfoil and a laminar oblique-shock reflection.
Abstract
The unstructured shock-fitting algorithm originally proposed in Ref. [3] has been further developed to make it capable of dealing with shock-wave/boundary-layer interactions [...]
- 38
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Evaluation of Different Computational Modelling Strategies of a Masonry Vault with Buttresses and Backfill
F. Gobbin, M. Malena, G. Felice, J. Lemos

WCCM-ECCOMAS2020.

Abstract
In this paper, a critical comparison of two of the most common methods for the analysis of masonry vaults up to collapse is carried on. Innovative 2D Discrete Element (DE) and Finite Element (FE) models have been adopted aiming at capturing the main features of masonry single curvature structures mechanical behavior. Two numerical strategies are adopted: a discrete element model and a continuous homogenized model. The first approach provides an estimate of the collapse load and failure pattern of masonry based on ad-hoc implemented algorithm. The second approach is formulated in the framework of multi-surface plasticity and implemented in a FE code for the path-following non-linear analysis of masonry wall described as continuous anisotropic plate. The two numerical approaches are adopted to reproduce the Experimental Campaign of a full-scale Catalan vault with buttresses and backfill, statically loaded at 1/3 span. The failure modes and the crack patterns obtained by the proposed models are compared between them and with that observed in the experimental test as well as the load-displacement response curves. Both the proposed models efficiently capture the behavior of the vault and, in particular, the backfill deformation and load-spreading effect, hinges position and formation order.
Abstract
In this paper, a critical comparison of two of the most common methods for the analysis of masonry vaults up to collapse is carried on. Innovative 2D Discrete Element (DE) [...]
- 23
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Simulation of Movement of the Device with Passive Vibration Isolation
I. Shardakov, I. Glot, A. Shestakov

WCCM-ECCOMAS2020.

Abstract
Modern electronic systems, computer hardware and navigation equipment on board moving objects can be subjected to significant mechanical impulse and vibrational impacts. These impacts can introduce additional errors in readings of devices, and sometimes lead to their mechanical failure. One of the effective ways to solve the problem is to apply the method of passive vibration protection, which makes it possible to reduce vibrations due to the use of damping elements. This paper examines the vibration response of a device mounted on a moving platform. The device is protected against vibration by 4 dampers. The platform is subjected to translational motions in three mutually orthogonal directions. This leads to the appearance of coupled translational and rotational vibrations of the protected unit. The problem is solved within the framework of the general theory of the dynamic of a rigid body. The paper presents the results of numerical experiments, in which the intensity of rotational vibrations of the protected unit is investigated depending on various mechanical characteristics of the system. Admissible variation of these characteristics, at which the angular acceleration of the protected unit remains below a limit value, has been determined.
Abstract
Modern electronic systems, computer hardware and navigation equipment on board moving objects can be subjected to significant mechanical impulse and vibrational impacts. These [...]
- 18
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Ontology Assisted Modelling of Galvanic Corrosion of Magnesium
D. Hoeche, N. Konchakova, M. Zheludkevich, T. Hagelien, J. Friis

WCCM-ECCOMAS2020.

Abstract
Multi-physics and multiscale modelling frameworks, especially for the computer based analysis of surface damage and corrosion, requires not only robust computational tools but also an efficient data-centric architecture for handling information exchange at different modelling scales. The issue to exchange data provided by different computational solvers as well as required and used in different programming languages forms a request in specific formats signifying a strong non-uniformity for an easy nexus with other solvers. This non-uniformity has created a need to focus on intermittent state-of-theart data-centric software tools, which aim to bridge data exchange technology, to ensure heterogeneity across a wide range of solvers [1]. Moreover, data organization in the form of ontological representation and metadata structures are necessary to be prepared as a standard for a coherent representation of information regardless of the diverse nature of data formats specific to a scientific discipline. A domain ontology based on the European Materials & Modelling Ontology (EMMO) for galvanic corrosion is outlined and connected to corresponding concepts in a galvanic corrosion model. This fundamental work provides and discusses the concept, underlying terminology and working mechanism of a data-centric architecture for exchanging and interfacing data-flow between data sources/sinks and solvers. It realizes an ontological representation of physics and chemistry of galvanic corrosion. Thus, it is a nuclei for further improvement's of interoperability between complex corrosion related phenomena and models. It paves the way for accurate computational corrosion engineering.
Abstract
Multi-physics and multiscale modelling frameworks, especially for the computer based analysis of surface damage and corrosion, requires not only robust computational tools [...]
- 66
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Cyclic Behaviour of Beam-Column Dowel Connection in Precast Elements
M. Moldovan, M. Nedelcu, Z. Kovacs

WCCM-ECCOMAS2020.

Abstract
Disruption of structural continuity due to the inherent nature of the connections poses a challenge in seismic design of precast concrete structures. Seismic behaviour of portal frame systems typically used for industrial halls, is greatly influenced by the beam-column connections. Capacity design dictates that these connections should have an elastic behaviour under seismic horizontal actions to allow for the dissipation mechanisms to develop in the desired area, in this case the base of the columns. If this connection fails, the entire structure is compromised and may lead to a premature, partial, or even total collapse. Efforts are currently underway for a better understanding of the seismic response of precast structures (e.g. SAFECAST project). In this study, the test setups tried to replicate as closely as possible the behaviour of a commonly used beam-column assembly connected by steel dowels. The test specimens were designed as full scale precast concrete elements. This experimental campaign aimed to determine the failure mechanisms of the assemblies and to check if capacity design requirements were satisfied. Three setups have been tested according to the experimental protocol described in the SAFECAST report. The first test specimen was subjected to a unidirectional monotonic loading protocol with the aim of observing the maximum failure force and deformation. The resulted maximum displacement was used to determine the displacement step increment for the cyclic loading protocol of the following two specimens. In all the cases, failure has occurred in the region of the dowel connection. The failure mechanism was either because of dowel yielding, concrete spalling around the dowel, or a combination of both, consistent with results obtained by other researchers. The results have showed that the column was far from reaching its failure capacity and a premature failure has occurred in the connection area, which should be avoided in common practice. Marius G.L. Moldovan, Mihai Nedelcu and Zsolt Kovacs
Abstract
Disruption of structural continuity due to the inherent nature of the connections poses a challenge in seismic design of precast concrete structures. Seismic behaviour of [...]
- 43
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On the Quantification of Discretization Uncertainty: Comparison of Two Paradigms
J. Bect, S. Zio, G. Perrin, C. Cannamela, E. Vazquez

WCCM-ECCOMAS2020.

Abstract
The use of simulation has spread to all areas of engineering and science, and the use of numerical models based on partial differential equations has thus multiplied. The resolution of these models is generally based on the discretization of the space in which the solutions to the equations under consideration are sought. The finite differences method or the finite elements method are two examples of such a discretization. This discretization simplifies the solving but implies a form of uncertainty on the value of any quantity of interest. To quantify this discretization uncertainty, the grid convergence index (GCI), based on the Richardson extrapolation technique, is now standard in the Verification and Validation (V&V) literature. But alternative approaches were also proposed in the statistical literature, such as Bayesian approaches with Gaussian process models. The objective of this work is to compare on a standard test case from the literature (Timoshenko's beam) the well-established GCI-based approach to the--younger--Bayesian approach for the quantification of discretization uncertainty.
Abstract
The use of simulation has spread to all areas of engineering and science, and the use of numerical models based on partial differential equations has thus multiplied. The [...]
- 50
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Estimation of Load-Time Curves Using Recurrent Neural Networks Based On Can Bus Signals
D. Herz, C. Krauß, C. Zimmerling, B. Grupp, F. Gauterin

WCCM-ECCOMAS2020.

Abstract
Precise knowledge of the load history of safety-relevant structures is a central aspect within the fatigue strength design of modern vehicles. Since the experimental measurement of load variables is complex and therefore associated with high costs, vehicles require estimation of these variables in order to design even more customer-orientedly in the future and thus consistently pursue sustainable lightweight construction. Hence the data measured by sensors in today's standard production vehicles is based on vehicle bus system signals which can be permanently retrieved. Due to the increasing availability of large quantities of recorded vehicle data, machine learning methods are moving into the focus of application. In this work, the implementation of Recurrent Neural Networks for the estimation of loadtime curves is investigated. In order to close existing gaps in the state of the art, successful concepts of machine learning for sequential data, such as speech processing, are to be transferred to this application case. Long Short-Term Memory cells [1] play a central role for this type of problem. In addition to the adaptation of the network architecture, the integration of engineering knowledge is pursued within the method development process in order to increase the quality of the model. Relevant input variables are specifically selected by feature engineering and new meaningful variables are generated by filtering. Statistical analysis is used to investigate the correlation of these input signals with the estimated quantities. The development of a robust load estimation takes place in the course of model development on the basis of the torque of the left-hand rear drive shaft. Results reveal that the Recurrent Neural Networks approach is justified in estimating the highly nonlinear load curve of a complexly loaded part as a component of the dynamic system by means of available sensor signals [2]. Subsequently, the model is validated using recorded measurement data for different chassis settings of the same vehicle. Finally, the transferability of the designed network configuration to other chassis components of the same vehicle is investigated and evaluated.
Abstract
Precise knowledge of the load history of safety-relevant structures is a central aspect within the fatigue strength design of modern vehicles. Since the experimental measurement [...]
- 50
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A Smeared Crack Modelling Approach for Aggregate Interlock and Mixed Mode Fracture of Concrete
J. Ungermann, V. Adam, J. Hegger, M. Claßen

WCCM-ECCOMAS2020.

Abstract
The intention of this contribution is the numerical description of the rarely investigated phenomenon of mixed mode fracture in plain concrete. Since cracks in concrete are typically subjected to both normal and shear displacements, a new material model called fictitious rough crack model (FRCM) is proposed which combines mode I fictitious crack models with aggregate interlock models. For modelling the mixed mode behavior as the result of coexisting cohesive concrete behavior and aggregate interlock stresses along concrete cracks, mode I behavior is considered as the main influence on crack formation at the crack tip and mode II behavior (aggregate interlock) is assumed to occur when translations are induced along the crack surfaces (slip). The combination of these tension-softening and shear-transfer laws and the resulting shear and normal stresses of both mechanisms in the crack characterizes the main idea of the model. Well-known experimental benchmark problems are solved both for validation of the proposed model as well as for comparison with renowned concrete models of commercial FE software. The analysis shows that the FRCM can simulate the transition from mode I fracture to mixed mode fracture in the structural response while the comparison with commercial numerical approaches demonstrates the lack of appropriate consideration of aggregate interlock and mixed mode behavior in commercial FE software.
Abstract
The intention of this contribution is the numerical description of the rarely investigated phenomenon of mixed mode fracture in plain concrete. Since cracks in concrete are [...]
- 115
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Hybrid Active Vibration Control in Wind Turbine Towers
N. Karnopp, H. Gomes

WCCM-ECCOMAS2020.

Abstract
Due to the demand for renewable and clean energy sources, the generation of electricity from wind farms has become a reality in Brazil. The central unit of energy generation in these farms are the wind turbines composed of tower, nacelle, and blades. Reduction in mass and material is always desirable in these units due to the final cost impact on a wind farm consisting of several units. The main external excitation source in these systems is the wind, or the system itself, as in the case of possible imbalance. The design of the support tower and foundations must take into account quasi-static stresses as well as the varying and transient stresses the system may be exposed in the service life, which could lead to fracture or fatigue problems. Minimizing the mass of these structures and keeping their vibration levels at acceptable values is a difficult task that can be achieved by controlling vibration either passively (with Dynamic Vibration Absorbers, DVA) or actively with actuators. This paper proposes to investigate the active vibration control for wind turbine systems with hybrid active vibration control. 1
Abstract
Due to the demand for renewable and clean energy sources, the generation of electricity from wind farms has become a reality in Brazil. The central unit of energy generation [...]
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Implementation and Validation of a Computationally Efficient DNS Solver for Reacting Flows in OpenFOAM
T. Zirwes, F. Zhang, P. Habisreuther, J. Denev, H. Bockhorn, D. Trimis

WCCM-ECCOMAS2020.

Abstract
To meet future climate goals, the efficiency of combustion devices has to be increased. This requires a better understanding of the underlying physics. The simulation of turbulent flames is a challenge because of the multi-scale nature of combustion processes: relevant length scales span over five orders of magnitude and time scales over more than ten. Because of this, the direct numerical simulation (DNS) of turbulent flames is only possible on large supercomputers. A DNS solver for chemically reacting flows implemented in the open-source framework OpenFOAM is presented. The thermo-chemical library Cantera is used to compute detailed transport coefficients based on kinetic gas theory. The multi-scale nature of time scales, which are much lower for the combustion chemistry than for the flow, are bridged by an operator splitting approach, which employs the open-source solver Sundials to integrate chemical reaction rates. Because the direct simulation of turbulent flames has to be performed on supercomputers, special care has been taken to improve the computational performance. A tool was developed which generates highly optimized C++ source code for the computation of chemical reaction rates. Additionally, a load balancing approach specifically made for the computation of chemical reaction rates is employed. In total, these optimizations can reduce total simulation times by up to 70 %. The accuracy of the new solver is assessed from different canonical testcases: 2D and 3D Taylor-Green vortex simulations show that the solver can reach up to fourth order convergence rates and that results differ by less than 1 % when compared to spectral DNS codes. Molecular diffusion and chemical reaction rates are compared to solutions of 1D flames from Cantera, showing perfect agreement. The solver is used to simulate the Sydney/Sandia burner. The simulation is performed on one of Germany's largest supercomputer on 28 800 CPU cores, employing 150 million cells and a chemical reaction mechanism with 19 species and about 200 reactions. Comparison with experimental data shows excellent agreement for time averaged and RMS values.
Abstract
To meet future climate goals, the efficiency of combustion devices has to be increased. This requires a better understanding of the underlying physics. The simulation of turbulent [...]
- 56
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Optimization of Inlet Valve Leaflet Shape Using Metamodel and Fluid-Structure Interaction
L. Pałys, M. Mrzygłód, M. Gawlikowski, R. Major

WCCM-ECCOMAS2020.

Abstract
Cardiac assist devices like continuous flow ventricular assist devices (CF-VAD) provide several benefits, including improved durability or higher energy efficiency. This paper presents the shape optimization for the inlet valve geometry of the pulsatile VAD using a metamodeling framework and fluid-structure interaction (FSI). The main task of the inlet valve is preventing the backflow to occur and keep proper valve washing as well as low hemolysis, induced by high shear stress. The finite element (FE) model of the valve was generated using a parametric model. The FE model was associated with a fluid flow analysis environment. The shear stress at wall leaflet structures was observed for all design points. For selected design variables, the minimization of the leaflet's wall shear stresses was carried out. As a result of optimization, the optimal valve leaflet shape was found. The developed modeling methodology can be easily adapted to investigate biomedical problems especially in the process of creating devices supporting cardiac circulation.
Abstract
Cardiac assist devices like continuous flow ventricular assist devices (CF-VAD) provide several benefits, including improved durability or higher energy efficiency. This paper [...]
- 33
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The One-Dimensional Turbulence Aspects of Internal Forced Convective Flows
J. Méndez, M. Klein, H. Schmidt

WCCM-ECCOMAS2020.

Abstract
We present an overview of issues for the modeling of internal forced convective flows with the One-Dimensional Turbulence (ODT) model. Results of recent research as well as prospective research issues are presented for statistically streamwise homogeneous flows and streamwise inhomogeneous mixed convective flows. The results illustrate the capabilities of the model to evaluate and bring insight into a wide range of physical phenomena in the field of convective flows. Nonetheless, as a model, ODT is best suited for the evaluation of asymptotically turbulent flows, i.e., away from laminar regimes.
Abstract
We present an overview of issues for the modeling of internal forced convective flows with the One-Dimensional Turbulence (ODT) model. Results of recent research as well as [...]
- 25
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Mesh Adaptation Using Adjoint Methods and Reduced-Order Models for Large Eddy Simulation
X. Li, S. Hulshoff, S. Hickel

WCCM-ECCOMAS2020.

Abstract
Adaptive mesh refinement (AMR) is potentially an effective way to automatically generate computational meshes for high-fidelity simulations such as Large Eddy Simulation (LES). Adjoint methods, which are able to localize error contributions, can be used to optimize the mesh for computing a physical quantity of interest (e.g. lift, drag) during AMR. When adjoint-based AMR techniques are applied to LES, primal flow solutions are needed to solve the adjoint problem backward in time due to the nonlinearity of Navier-Stokes equations. However, the resources required to store primal flow solutions can be huge, even prohibitive, in practical problems because of the long averaging time for computing statistical quantities. In this paper, a Reduced-Order Model (ROM) based upon Proper Orthogonal Decomposition (POD) is introduced to circumvent this issue. First, an adjoint-based error estimation procedure is verified using a manufactured solution. Then a ROM-driven AMR strategy is studied using a LES model problem based on the 1D unsteady Burgers equation. Numerical results demonstrate that using ROMs not only lowers storage requirements, but also has no impact on the effectiveness of adjoint-based AMR.
Abstract
Adaptive mesh refinement (AMR) is potentially an effective way to automatically generate computational meshes for high-fidelity simulations such as Large Eddy Simulation (LES). [...]
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Comparative Study of Inner-Outer Krylov Solvers for Linear Systems in Structured and High-Order Unstructured CFD Problems
M. Jadoui, C. Blondeau, E. Martin, F. Renac, F. Roux

WCCM-ECCOMAS2020.

Abstract
Advanced Krylov subspace methods are investigated for the solution of linear systems arising from an adjoint-based aerodynamic shape optimization problem. A special attention is paid for the flexible inner-outer GMRES strategy combined with most relevant preconditioning strategies and deflation techniques. The choice of this specific class of Krylov solvers for solving challenging problems is based on its outstanding convergence properties. Moreover, parallel scalability is improved by globalizing the preconditioning phase through an additive domain decomposition technique. However, maintaining the performance of the preconditioner may be challenging since scalability and efficiency of a preconditioning technique are properties often antagonistic to each other. We demonstrate how flexible inner-outer Krylov methods are able to overcome this critical issue. A numerical comparative study is provided on the supercritical OAT15A airfoil in turbulent flow under transonic regime conditions using a Finite Volume method (FV) and a High-Order Discontinuous Galerkin (DG) one. Based on this representative problem a discussion of the recommended numerical practices is proposed.
Abstract
Advanced Krylov subspace methods are investigated for the solution of linear systems arising from an adjoint-based aerodynamic shape optimization problem. A special attention [...]
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On a Projection Method for the Numerical Integration of Constitutive Equations Involving Large Inelastic and Incompressible Deformations
M. Sielenkämper, J. Dittmann, S. Wulfinghoff

WCCM-ECCOMAS2020.

Abstract
Finite deformation plasticity often involves the multiplicative split of the deformation gradient into an elastic and plastic part. Motivated by observations in physics, the plastic part is assumed to be volume preserving, i.e., the plastic part of the deformation gradient is unimodular. In order to not accumulate errors, in the best case, one fulfills this constraint exactly to obtain accurate results (see, e.g., [3]). While other approaches where pursued as well, many authors therefore adopted the use of the exponential map, which is a geometric integrator preserving the plastic incompressibility. However, it's computation is not straightforward and performing the eigenvalue decomposition and it's linearization for the exponential function is numerically elaborate. Therefore, in this work, a new approach which also exactly preserves the incompressibility constraint is developed. It makes use of a projection of all symmetric tensors onto the manifold of unimodular tensors. The proposed method is compared to models utilizing the exponential map in numerical experiments.
Abstract
Finite deformation plasticity often involves the multiplicative split of the deformation gradient into an elastic and plastic part. Motivated by observations in physics, the [...]
- 17
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An Immersed Boundary Method Based Fluid-Structure Interaction Solver with Applications in Energy Harvesting
G. Sharma, R. Bhardwaj

WCCM-ECCOMAS2020.

Abstract
We present the development of an in-house fluid-structure interaction (FSI) solver and employ the solver for state-of-the-art applications in energy harvesting. An implicit partitioned approach is utilized to couple a sharp-interface immersed boundary method based flow solver and a finite-element method based structural solver. The code validations are presented for large-scale flow-induced deformation and vortex-induced vibration of an elastically mounted circular cylinder. We employ the FSI solver for analysis of vortex-induced vibration (VIV) of a cylinders, with different cross-sections. The suppression and agitation of VIV for different cylinders are discussed along with lock-in characteristics. An energy harvesting model is utilized to estimate the power generated per unit mass and it was found that the galloping of the D-cylinder is useful for broadband energy harvesting for a wide range of reduced velocities.
Abstract
We present the development of an in-house fluid-structure interaction (FSI) solver and employ the solver for state-of-the-art applications in energy harvesting. An implicit [...]
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Optimal Pressure Boundary Control of Steady Multiscale Fluid-Structure Interaction Shell Model Derived From Koiter Equations
A. Chierici, L. Chirco, V. Giovacchini, S. Manservisi, E. Marzi

WCCM-ECCOMAS2020.

Abstract
The fluid-structure interaction (FSI) problem has been extensively studied, and many papers and books are available in the literature on the subject. In this work, we consider some optimal FSI pressure boundary control applications by using a membrane model derived from the Koiter shell equations where the thickness of the solid wall can be neglected and the computational cost of the numerical problem reduced. We study the inverse problem with the aim of achieving a certain objective by changing some design parameters (e.g. forces, boundary conditions or geometrical domain shapes) by using an optimal control approach based on Lagrange multipliers and adjoint variables. In particular, a pressure boundary optimal control is presented in this work. The optimality system is derived from the first-order optimality condition by taking the Fréchet derivatives of the Lagrangian with respect to all the variables involved. This system is solved by using a finite element code with mesh-moving capabilities. In order to support the proposed approach, we perform numerical tests where the pressure on a fluid domain boundary controls the displacement that occurs in a well-defined region of the solid domain.
Abstract
The fluid-structure interaction (FSI) problem has been extensively studied, and many papers and books are available in the literature on the subject. In this work, we consider [...]
- 16
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A Comparison Of Different Technologies For Thrust Vectoring In A Linear Aerospike
M. Ferlauto, A. Ferrero, M. Marsicovetere, R. Marsilio

WCCM-ECCOMAS2020.

Abstract
The aerospike nozzle represents an interesting technology for Single-Stage-To-Orbit vehicles because of its self-adapting capability. It is possible to get thrust vectoring capabilities in different ways. A straightforward solution consists in applying differential throttling to multiple combustion chambers which feed the nozzle. An alternative technology, which can be used in the presence of a common combustion chamber, is represented by fluidic thrust vectoring which requires the injection of a secondary flow from a slot on the wall. In this work, the flow field in a linear aerospike nozzle is numerically investigated by means of RANS simulations and both differential throttling and shock vectoring are studied. A parametric study is performed to evaluate the potential of the two technologies.
Abstract
The aerospike nozzle represents an interesting technology for Single-Stage-To-Orbit vehicles because of its self-adapting capability. It is possible to get thrust vectoring [...]
- 23
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A Subcell Finite Volume Positivity-Preserving Limiter for DGSEM Discretizations of the Euler Equations
A. Rueda-Ramírez, G. Gassner

WCCM-ECCOMAS2020.

Abstract
In this paper, we present a positivity-preserving limiter for nodal Discontinuous Galerkin disctretizations of the compressible Euler equations. We use a Legendre-Gauss-Lobatto (LGL) Discontinuous Galerkin Spectral Element Method (DGSEM) and blend it locally with a consistent LGL-subcell Finite Volume (FV) discretization using a hybrid FV/DGSEM scheme that was recently proposed for entropy stable shock capturing. We show that our strategy is able to ensure robust simulations with positive density and pressure when using the standard and the split-form DGSEM. Furthermore, we show the applicability of our FV positivity limiter in extremely under-resolved vortex dominated simulations and in problems with shocks.
Abstract
In this paper, we present a positivity-preserving limiter for nodal Discontinuous Galerkin disctretizations of the compressible Euler equations. We use a Legendre-Gauss-Lobatto [...]
- 35
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The Cohesive Granular Collapse as a Continuum : Parametrization Study
A. Abramian, L. Staron, P. Lagrée

WCCM-ECCOMAS2020.

Abstract
Although intensive research on the flow of dry granular materials has allowed for the proposition of continuum rheology and modelling, the behaviour of flowing cohesive material has attracted less attention so far. To start modelling such cohesive flows, we first focus on the configuration of a granular collapse, which is a simple benchmark test. Specifically, we compare granular-collapse experiments of cohesive grains with numerical simulations, where we test a simple rheology for the material : the so-called µ(I)-rheology, supplmented by a yield stress for cohesion. This document reports the sensitivity of our numerical simulations on the parameters of the rheology, often challenging to measure in experiments.
Abstract
Although intensive research on the flow of dry granular materials has allowed for the proposition of continuum rheology and modelling, the behaviour of flowing cohesive material [...]
- 24
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Scalable Newton-Krylov-BDDC and FETI-DP Deluxe Solvers for Decoupled Cardiac Reaction-Diffusion Models
N. Huynh, L. Pavarino, S. Scacchi

WCCM-ECCOMAS2020.

Abstract
Two parallel Newton-Krylov Balancing Domain Decomposition by Constraints (BDDC) and Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) solvers are analyzed and numerically studied for implicit time discretizations of the Bidomain equations. This system models the cardiac bioelectrical activity and it consists of a degenerate system of two non-linear reaction-diffusion partial differential equations (PDEs), coupled with a stiff system of ordinary differential equations (ODEs). A non-linear algebraic system arises from a finite element discretization in space and an implicit discretization in time, based on decoupling the PDEs from the ODEs. Within each Newton iteration, the Jacobian linear system is solved by a Krylov method, accelerated by BDDC or FETI-DP preconditioners, both augmented with the recently introduced deluxe scaling of the dual variables. Several parallel numerical tests on Linux clusters confirm a novel polylogarithmic convergence rate bound, showing scalability and quasi-optimality of the proposed solvers.
Abstract
Two parallel Newton-Krylov Balancing Domain Decomposition by Constraints (BDDC) and Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) solvers are analyzed and [...]
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Numerical Modeling Of Two-Phase Flow With Contact Discontinuities
R. Remmerswaal, A. Veldman

WCCM-ECCOMAS2020.

Abstract
When simulating high Reynolds number two-phase flow, boundary layers develop at the interface, which are much thinner compared to the capillary length-scales that are of interest. Resolving such an interface layer is expensive and therefore it is often not resolved in a simulation. Numerically such an underresolved interface layer results in a velocity discontinuity tangential to the interface. We propose to include such tangential velocity discontinuities in our numerical model. This results in a sharp two-fluid model for two-phase flow, where only the interface-normal component of the velocity field is smooth. This condition is implicitly enforced via a new jump condition on the pressure gradient, which we discretize using a multidimensional variant of the ghost fluid method [6]. Results are shown of breaking waves [2] as well as (breaking) waves impacting a solid wall [3] where we compare to state-of-the-art methods [3, 4]. We show that our proposed method is able to accurately simulate high Reynolds number two-phase flow without the need for resolving, or artificially thickening, of the interface layer.
Abstract
When simulating high Reynolds number two-phase flow, boundary layers develop at the interface, which are much thinner compared to the capillary length-scales that are of interest. [...]
- 15
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Parallel Unstructured Mesh Adaptation Based on Iterative Remeshing and Repartitioning
L. Cirrottola, A. Froehly

WCCM-ECCOMAS2020.

Abstract
We present a parallel unstructured mesh adaptation algorithm based on iterative remeshing and mesh repartitioning. The algorithm rests on a two-level parallelization scheme allowing to tweak the mesh group size for remeshing, and on a mesh repartitioning scheme based on interface displacement by front advancement. The numerical procedure is implemented in the open source ParMmg software package. It enables the reuse of existing sequential remeshing libraries, a non-intrusive linkage with thirdparty solvers, and a tunable exploitation of distributed parallel environments. We show the efficiency of the approach by comparing interface displacement repartitioning with graph-based repartitioning, and by showing isotropic weak-scaling tests and preliminary anisotropic tests.
Abstract
We present a parallel unstructured mesh adaptation algorithm based on iterative remeshing and mesh repartitioning. The algorithm rests on a two-level parallelization scheme [...]
- 10
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NLFK4ALL: An Open-Source Demostration Toolbox for Computationally Efficient Nonlinear Froude-Krylov Force Calculations
G. Giorgi, G. Bracco, G. Mattiazzo

WCCM-ECCOMAS2020.

Abstract
Accurate modelling of wave-structure interaction is essential for a successful and reliable design of offshore structures and their ancillary systems. However, the fidelity of mathematical models is challenged when nonlinearities become significant, i.e. when the floater operates in severe sea states and/or it shows large dynamic responses compared to the incoming wave. This is normally the case for wave energy converters (WECs) because large motions are desirable for better power extraction, while conventional offshore structures are usually designed to prevent large responses and ensure stability. Fastcomputation is a further mandatory requirement for mathematical models that are used for design purposes. This is particularly true for wave energy applications, since extensive parametric studies are needed to minimize the cost of energy, i.e. increase power extraction capabilities while limiting capital and operational expenditures. Furthermore, model-based control strategies, essential for substantial increase of the WEC performance, require representative mathematical models. The requirements of accuracy and low computational time are usually contrasting, so an appropriate compromise should be defined. This paper proposes a nonlinear Froude-Krylov (NLFK) force model for axisymmetric floaters. The symmetry of the geometry (common for WECs) is exploited to achieve a low computational time (about real-time computation). Furthermore, since NLFK forces are the main nonlinearities for such devices, the obtained accuracy is higher than linear models. An open-source Matlab demonstration toolbox is introduced, called NLFK4ALL (doi: 10.5281/zenodo.3544848), which provides a ready-to-use implementation of the NLFK approach in six degrees of freedom. Accuracy and computational aspects of the method are here discussed, such as the complexity of the analytical description of the intersection between free surface elevation and the floater, and the impact of tolerances on the convergence of the numerical integration.
Abstract
Accurate modelling of wave-structure interaction is essential for a successful and reliable design of offshore structures and their ancillary systems. However, the fidelity [...]
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Experimental Testing Correlation with Numerical Meso-Scale Modelling of CFRP Structures and the Significance to Virtual Certification of Airfames
C. Moulkiotis, I. Giannopoulos, E. Theotokoglou

WCCM-ECCOMAS2020.

Abstract
The design of structural components has altered fundamentally since laminated composites were proved excellent candidate materials in aerospace applications. The key aspects rendering CFRPs preferable to metals, are mostly their significantly higher specific mechanical properties, and the design flexibility through the stacking sequence selection. However, the currently in use limit and polynomial failure criteria, are inadequate to accurately predict all experimentally observed failure modes and damage specificities of the lamina individual constituents, imposing difficulties in the numerical certification of airframe composites. Thus, component and lamina-level testing are sometimes inevitable, requiring industrial resources which are expensive as well as environmentally costly. For that reason, virtual testing could be more promising in substituting real experimental testing, if conducted under advanced failure criteria which better describe the nature of failure. In this study, the open hole tensile (OHT) test has been simulated under the LaRC05 phenomenological failure criterion, with embedded strain-based progressive damage material behavior. A relatively common composite material in aerospace structures has been selected, IM7 8552 of Hexcel, to compare the numerical strength predictions with its corresponding experimental values. The simulations carried out are based on a standard test method by ASTM international, which address the standardisation of strength tests of polymer matrix composite laminates. The, model was created in ABAQUS/Explicit under the VUMAT user subroutine. The resulted predictions have been found to well correlate with the testing data, irrespective the specimen stacking sequence.
Abstract
The design of structural components has altered fundamentally since laminated composites were proved excellent candidate materials in aerospace applications. The key aspects [...]
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Flexible Discretization for Computational Aeroacoustics
M. Kaltenbacher, J. Heinz, K. Roppert, S. Schoder

WCCM-ECCOMAS2020.

Abstract
This contribution discusses the capabilities of non-conforming grid techniques to allow an optimal discretization for each subdomain. In doing so, we derive the Nitsche-type mortaring formulation for the acoustic wave equation, which incorporates the physical transmission condition of continuity of acoustic pressure and its flux being the normal component of the acoustic particle velocity. The Nitschetype mortaring handles the coupling by symmetrizing the bilinear form and adding an appropriate jump term. The simulation of the edge tone demonstrates the applicability and superiority of non-conforming grids for computational aeroacoustics at low Mach numbers compared to conforming finite element methods.
Abstract
This contribution discusses the capabilities of non-conforming grid techniques to allow an optimal discretization for each subdomain. In doing so, we derive the Nitsche-type [...]
- 46
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Benchmarking the P-MLQMC method on a geotechnical engineering problem
P. Blondeel, P. Robbe, S. François, G. Lombaert, S. Vandewalle

WCCM-ECCOMAS2020.

Abstract
Problems in civil engineering are often characterized by significant uncertainty in their material parameters. Sampling methods are a straightforward manner to account for this uncertainty, which is typically modeled as a random field. A novel method developed by the authors called p-refined Multilevel Quasi-Monte Carlo (p-MLQMC), achieves a significant computational cost reduction with respect to classic Multilevel Monte Carlo (h-MLMC). p-MLQMC uses a hierarchy of p-refined Finite Element meshes, combined with a deterministic Quasi-Monte Carlo (QMC) sampling rule. A non-negligible part of modeling the stochastics in non-deterministic engineering problems consists in adequately incorporating the uncertainty in the Finite Element model. This is typically done by evaluating the random field at certain carefully chosen evaluation points, and assigning the resulting scalars to the different finite elements. For the h-MLMC method, these evaluation points consist of the centroids of the elements. For the p-MLQMC method, we distinguish two different approaches to select the evaluation points, the Non-Nested Approach (NNA) and the Local Nested Approach(LNA). We investigate how these approaches affect the variance reduction over the levels and the total computational cost. We benchmark the p-ML(Q)MC-LNA, p-ML(Q)MC-NNA and h-MLMC method on a slope stability problem where the uncertainty is located in the soil's cohesion. We show that the p-MLQMC-LNA method outperforms all other considered methods in terms of computational cost.
Abstract
Problems in civil engineering are often characterized by significant uncertainty in their material parameters. Sampling methods are a straightforward manner to account for [...]
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Numerical Analysis of Oscillatory Flows in the Human Brain by a Lattice-Boltzmann Method
S. Koh, J. Kim, A. Lintermann

WCCM-ECCOMAS2020.

Abstract
The cerebrospinal fluid flow in a brain ventricular system is analyzed by the numerical approach employing a lattice-Boltzmann (LB) method. The cerebrospinal fluid, which surrounds the human brain and spinal cord, fills the cerebral ventricles as well as the cranial and subarachnoid spaces. Diseases in a central nerve system disrupt the flow circulation which influences on a number of vital functions. A computational fluid dynamics technique is used to determine the member geometry impact on the flow motion. The numerical analysis focuses on building a simulation-based basis for testing/optimizing therapeutical methods and understanding the pathophysiology. Magnetic resonance (MR) imaging is exploited to obtain realistic geometries in a brain ventricular system. The computational domain is discretized by a hierarchical Cartesian octree mesh. The numerical procedure based on an LB method overcomes the difficulties raised by typical finite-difference and finite-volume methods on high-performance computing (HPC) systems. An oscillating flow boundary condition is defined to resolve the kinetic behavior of cerebrospinal fluid in a cardiac cycle. The three-dimensional structures captured in the cerebral ventricles show a qualitative agreement with an observation based on an MR velocity mapping. The simulation on a HPC system is able to provide further insights into the transport from brain to spinal cord.
Abstract
The cerebrospinal fluid flow in a brain ventricular system is analyzed by the numerical approach employing a lattice-Boltzmann (LB) method. The cerebrospinal fluid, which [...]
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