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Documents published in Scipedia

• Simulating squeeze flows in multiaxial laminates: towards fully 3D mixed formulations

  R. Pinillo, E. Abisset-Chavanne, F. Chinesta, A. Huerta

  Int. J. Material Forming (2017). Vol. 10 (5), pp. 653-359

  
  

  Abstract

  Thermoplastic composites are widely considered in structural parts. In this paper attention is paid to squeeze flow of continuous fiber laminates. In the case of unidirectional prepregs, the ply constitutive equation is modeled as a transversally isotropic fluid, that must satisfy both the fiber inextensibility as well as the fluid incompressibility. When laminate is squeezed the flow kinematics exhibits a complex dependency along the laminate thickness requiring a detailed velocity description through the thickness. In a former work the solution making use of an in-plane-out-of-plane separated representation within the PGD – Poper Generalized Decomposition – framework was successfully accomplished when both kinematic constraints (inextensibility and incompressibility) were introduced using a penalty formulation for circumventing the LBB constraints. However, such a formulation makes difficult the calculation on fiber tractions and compression forces, the last required in rheological characterizations. In this paper the former penalty formulation is substituted by a mixed formulation that makes use of two Lagrange multipliers, while addressing the LBB stability conditions within the separated representation framework, questions never until now addressed.

  Abstract
  Thermoplastic composites are widely considered in structural parts. In this paper attention is paid to squeeze flow of continuous fiber laminates. In the case of unidirectional [...]

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• Vademecum-based GFEM (V-GFEM): optimal enrichment for transient problems

  D. Canales, A. Leygue, F. Chinesta, D. González, E. Cueto, E. Feulvarch, J. Bergheau, A. Huerta

  Comput. Methods Appl. Mech. Engrg., (2016). Vol. 108 (9), pp. 971-989 (Preprint)

  
  

  Abstract

  This paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off-line and stored in memory in the form of a computational vademecum so that they can be used on-line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum-generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes.

  Abstract
  This paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off-line [...]

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• Real-time simulation techniques for augmented learning in science and engineering

  C. Quesada, D. González, I. Ruiz, E. Cueto, A. Huerta, F. Chinesta

  The visual computer (2016). Vol. 32 (11), pp. 1465-1479

  
  

  Abstract

  In this paper we present the basics of a novel methodology for the development of simulation-based and augmented learning tools in the context of applied science and engineering. It is based on the extensive use of model order reduction, and particularly, of the so-called Proper Generalized Decomposition (PGD) method. This method provides a sort of meta-modeling tool without the need for prior computer experiments that allows the user to obtain real-time response in the solution of complex engineering or physical problems. This real-time capability also allows for its implementation in deployed, touch-screen, handheld devices or even to be immersed into electronic textbooks. We explore here the basics of the proposed methodology and give examples on a few challenging applications never until now explored, up to our knowledge.

  Abstract
  In this paper we present the basics of a novel methodology for the development of simulation-based and augmented learning tools in the context of applied science and engineering. [...]

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• Elliptic harbor wave model with perfectly matched layer and exterior bathymetry effects

  D. Modesto, S. Fernández-Méndez, A. Huerta

  Journal of Waterway, port, coastal and ocean engineering (2016). Vol. 142 (5), pp. 04016008-1/04016008-14 (Preprint)

  
  

  Abstract

  Standard strategies for dealing with the Sommerfeld condition in elliptic mild-slope models require strong assumptions on the wave field in the region exterior to the computational domain. More precisely, constant bathymetry along (and beyond) the open boundary, and parabolic approximations–based boundary conditions are usually imposed. Generally, these restrictions require large computational domains, implying higher costs for the numerical solver. An alternative method for coastal/harbor applications is proposed here. This approach is based on a perfectly matched layer (PML) that incorporates the effects of the exterior bathymetry. The model only requires constant exterior depth in the alongshore direction, a common approach used for idealizing the exterior bathymetry in elliptic models. In opposition to standard open boundary conditions for mild-slope models, the features of the proposed PML approach include (1) completely noncollinear coastlines, (2) better representation of the real unbounded domain using two different lateral sections to define the exterior bathymetry, and (3) the generation of reliable solutions for any incoming wave direction in a small computational domain. Numerical results of synthetic tests demonstrate that solutions are not significantly perturbed when open boundaries are placed close to the area of interest. In more complex problems, this provides important performance improvements in computational time, as shown for a real application of harbor agitation.

  Abstract
  Standard strategies for dealing with the Sommerfeld condition in elliptic mild-slope models require strong assumptions on the wave field in the region exterior to the computational [...]

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• Space‐time NURBS‐enhanced finite elements for free‐surface flows in 2D

  A. Stavrev, P. Knechtges, S. Elgeti, A. Huerta

  Int. J. Numer. Meth. Fluids (2016). Vol. 81 (7), pp. 426-450

  
  

  Abstract

  The accuracy of numerical simulations of free‐surface flows depends strongly on the computation of geometric quantities like normal vectors and curvatures. This geometrical information is additional to the actual degrees of freedom and usually requires a much finer discretization of the computational domain than the flow solution itself. Therefore, the utilization of a numerical method, which uses standard functions to discretize the unknown function in combination with an enhanced geometry representation is a natural step to improve the simulation efficiency. An example of such method is the NURBS‐enhanced finite element method (NEFEM), recently proposed by Sevilla et al. The current paper discusses the extension of the spatial NEFEM to space‐time methods and investigates the application of space‐time NURBS‐enhanced elements to free‐surface flows. Derived is also a kinematic rule for the NURBS motion in time, which is able to preserve mass conservation over time. Numerical examples show the ability of the space‐time NEFEM to account for both pressure discontinuities and surface tension effects and compute smooth free‐surface forms. For these examples, the advantages of the NEFEM compared with the classical FEM are shown. 

  Abstract
  The accuracy of numerical simulations of free‐surface flows depends strongly on the computation of geometric quantities like normal vectors and curvatures. This geometrical [...]

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• Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: application to harbor agitation

  D. Modesto, S. Zlotnik, A. Huerta

  Comput. Methods Appl. Mech. Engrg., (2015). Vol. 295, pp. 127-149 (Preprint)

  
  

  Abstract

  Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular nature of the Helmholtz operator and the sensibility of the solution to small variations of the data. Here a reduced order model is used to determine the scattered solution everywhere in the domain for any incoming wave direction and frequency. Moreover, this is applied to a real engineering problem: water agitation inside real harbors for low to mid-high frequencies. The Proper Generalized Decomposition (PGD) model reduction approach is used to obtain a separable representation of the solution at any point and for any incoming wave direction and frequency. Here, its applicability to such a problem is discussed and demonstrated. More precisely, the contributions of the paper include the PGD implementation into a Perfectly Matched Layer framework to model the unbounded domain, and the separability of the operator which is addressed here using an efficient higher-order projection scheme. Then, the performance of the PGD in this framework is discussed and improved using the higher-order projection and a Petrov-Galerkin approach to construct the separated basis. Moreover, the efficiency of the higherorder projection scheme is demonstrated and compared with the higher-order singular value decomposition.

  Abstract
  Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular [...]

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• Real-time monitoring of thermal processes by reduced order modeling

  J. Aguado, A. Huerta, F. Chinesta, E. Cueto

  Int. J. Numer. Meth. Engng. (2015). Vol. 102 (5), pp. 991-1017 (Preprint)

  
  

  Abstract

  This work presents a simple technique for real-time monitoring of thermal processes. Real-time simulationbased control of thermal processes is a big challenge because high-fidelity numerical simulations are costly and cannot be used, in general, for real-time decision making. Very often, processes are monitored or controlled with a few measurements at some specific points. Thus, the strategy presented here is centered on fast evaluation of the response only where it is needed. To accomplish this, classical harmonic analysis is combined with recent model reduction techniques. This leads to an advanced harmonic methodology, which solves in real-time the transient heat equation at the monitored point. In order to apply the reciprocity principle, harmonic analysis is used in the space-frequency domain. Then, Proper Generalized Decomposition, a reduced order approach, pre-computes a transfer function able to produce the output response for a given excitation. This transfer function is computed offline and only once. The response at the monitoring point can be recovered performing a computationally inexpensive post-processing step. This last step can be performed online for real-time monitoring of the thermal process. Examples show the applicability of this approach for a wide range of problems ranging from fast temperature evaluation to inverse problems.

  Abstract
  This work presents a simple technique for real-time monitoring of thermal processes. Real-time simulationbased control of thermal processes is a big challenge because high-fidelity [...]

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• Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations

  G. Giorgiani, S. Fernández-Méndez, A. Huerta

  Computers and Fluids (2014). Vol. 98, pp. 196-208 (Preprint)

  
  

  Abstract

  A degree adaptive Hybridizable Discontinuous Galerkin (HDG) method for the solution of the incompressible Navier-Stokes equations is presented. The key ingredient is an accurate and computationally inexpensive a posteriori error estimator based on the super-convergence properties of HDG. The error estimator drives the local modification of the approximation degree in the elements and faces of the mesh, aimed at obtaining a uniform error distribution below a user-given tolerance in a given output of interest. Three 2D numerical examples are presented. High efficiency of the proposed error estimator is found, and an important reduction of the computational effort is shown with respect to non-adaptive computations, both for steady state and transient simulations.

  Abstract
  A degree adaptive Hybridizable Discontinuous Galerkin (HDG) method for the solution of the incompressible Navier-Stokes equations is presented. The key ingredient is an accurate [...]

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• On the natural stabilization of convection dominated problems using high order Bubnov–Galerkin finite elements

  Q. Cai, S. Kollmannsberger, E. Sala-Lardies, A. Huerta, E. Rank

  Computers & Mathematics with Applications (2014). Vol. 66 (12), pp. 2545-2558

  
  

  Abstract

  In the case of dominating convection, standard Bubnov–Galerkin finite elements are known to deliver oscillating discrete solutions for the convection–diffusion equation. This paper demonstrates that increasing the polynomial degree (p-extension) limits these artificial numerical oscillations. This is contrary to a widespread notion that an increase of the polynomial degree destabilizes the discrete solution. This treatise also provides explicit expressions as to which polynomial degree is sufficiently high to obtain stable solutions for a given Péclet number at the nodes of a mesh.

  Abstract
  In the case of dominating convection, standard Bubnov–Galerkin finite elements are known to deliver oscillating discrete solutions for the convection–diffusion [...]

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• Parametric solutions involving geometry: a step towards efficient shape optimization

  A. Ammar, A. Huerta, F. Chinesta, E. Cueto, A. Leygue

  Comput. Methods Appl. Mech. Engrg., (2014). Vol. 268, pp. 178-193

  
  

  Abstract

  Optimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition (PGD) introduced in former works, which is applied here to compute geometrically parametrized solutions

  Abstract
  Optimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual [...]

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