Documents published in Scipedia

• On the iterative solution of saddle point problems using a symmetric positive definite preconditioner

  P. Devloo, G. Avancini, M. Meneghel

  WCCM2024.

  
  

  Abstract

  Saddle point problems frequently appear in many mathematical and engineering applications. Most systems of partial differential equations with constraints give rise to saddle point linear systems. Typical examples include mixed finite element formulations to solve fluid flows and/or elasticity problems under full incompressibility. The inversion of saddle point problems is challenging due to inherent numerical instability in the direct inversion methods. Many direct and iterative methods have been proposed to overcome this challenges, such as the Schur complement and the Uzawa’s method. In the context of mixed finite element for incompressible flows using stable H(div)-L2 spaces for velocity and pressure, we propose an iterative method that can effectively solve a saddle point problem iteratively by summing a small compressibility to the original matrix. The preconditioning matrix is symmetric positive definite, which allows the usage of Cholesky decomposition and/or CG-like iterative solvers to compute the incremental solution for the velocities unknowns. A procedure to compute the average pressure of each element of the incompressible problem is developed using the unbalanced fluxes caused by the compressibility perturbation. The average is updated during the iterative process as a function of the velocity increment at each iteration.

  Abstract
  Saddle point problems frequently appear in many mathematical and engineering applications. Most systems of partial differential equations with constraints give rise to saddle [...]

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• Effect of the capillary force on the repose angle of granular materials

  W. Ziye, T. Yong

  WCCM2024.

  
  

  Abstract

  The angle of repose does affect the behavior of granular materials and has a wide range of applications. The addition of a small amount of liquid can dramatically change the properties of granular media, leading to an increase in the repose angle. This change is mainly attributed to the capillary force resulting from the liquid bridge when the small amount of water was introduced. The capillary force as an attractive force increases the interaction between particles and becomes a dominant factor affecting the angle of repose because it is usually stronger than gravity. In this paper, a new discrete element method (DEM) model was developed in which the capillary force was calculated by the liquid bridge model based on toroidal approximation. The developed DEM model linked the microscopic liquid bridge volume to the macroscopic water content and it also considered the effect of liquid bridge breakage and formation on capillary force. The numerical model was first validated by comparing the experimental and numerical results. Then, the effects of surface tension, volume of the liquid bridge, and the contact angle are studied numerically. Finally, the empirical equation between water content and angle of repose is given under the present simulation conditions. This work will provide a deep understanding for the effect of capillary on the angle of repose.

  Abstract
  The angle of repose does affect the behavior of granular materials and has a wide range of applications. The addition of a small amount of liquid can dramatically change the [...]

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• Model-based design approach finding optimal liquid cooling flow path for electric vehicle battery

  D. Aketo, K. Ono

  WCCM2024.

  
  

  Abstract

  Today many electronic devices that generate significant heat are required to be equipped with liquid cooling systems to reduce their temperature. Since the liquid flow path in the cooling system affects cooling performance, determining flow path in the early development phase can improve the efficiency of the downstream development process and reduce the total cost. In this paper, we propose a model-based analysis system for thermo-fluid phenomena based on CFD results and demonstrate the parametric optimization of flow path.

  Abstract
  Today many electronic devices that generate significant heat are required to be equipped with liquid cooling systems to reduce their temperature. Since the liquid flow path [...]

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• Input-output reduced order modeling for public health intervention evaluation

  A. Viguerie, E. Jacobson, C. Piazzola

  WCCM2024.

  
  

  Abstract

  In recent years, mathematical models have become an indispensable tool in the planning, evaluation, and implementation of public health interventions. Models must often provide detailed information for many levels of population stratification. Such detail comes at a price: in addition to the computational costs, the number of considered input parameters can be large, making effective study design difficult. To address these difficulties, we propose a novel technique to reduce the dimension of the model input space to simplify model-informed intervention planning. The method works by first applying a dimension reduction technique on the model output space. We then develop a method which allows us to map each reduced output to a corresponding vector in the input space, thereby reducing its dimension. We apply the method to the HIV Optimization and Prevention Economics (HOPE) model, to validate the approach and establish proof of concept.

  Abstract
  In recent years, mathematical models have become an indispensable tool in the planning, evaluation, and implementation of public health interventions. Models must often provide [...]

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• Computational model for local buckling of compressively loaded omega-stringer-stiffened panels

  C. El Yaakoubi-Mesbah, C. Mittelstedt

  WCCM2024.

  
  

  Abstract

  Thin-walled composite structures are used in applications such as aircraft and spacecraft due to their low weight and corresponding high stiffness properties. To optimize the potential of these structures to the fullest extent, a complete understanding of their stability behavior is required. Thereby, uniaxial compression describes an important load case that is investigated. A closed-form analytical method based on the energy method for determining the local buckling load of omega-stringer-stiffened panels is presented. The stiffened panel under consideration consists of the skin plate with eccentrically attached stringer feet along the longitudinal sides of the panel, while the remaining part of the omega-stringer is modeled by corresponding elastically restrained edges. Due to the applied stringer feet, stiffness discontinuities occur in the stiffened panel. This is covered by the presented method, whereas in comparable studies in the literature, a homogeneous stiffness is often assumed across the entire panel. To evaluate the new analysis method, a comparison with the numerical solution of the corresponding Levy-type ´solution and the finite element analysis is being drawn.

  Abstract
  Thin-walled composite structures are used in applications such as aircraft and spacecraft due to their low weight and corresponding high stiffness properties. To optimize [...]

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• Developments in the use of the Bonded Particle Model to study ore fracture

  T. Oladele, D. Weatherley, L. Bbosa

  WCCM2024.

  
  

  Abstract

  In mineral processing, ore fracture is an essential first step for which the objective is to increase the exposed surface area of the valuable mineral, thereby increasing the likelihood of liberation in subsequent separation stages. This process is well known to be energy-intensive, and increasing scrutiny around sustainable practices has heightened the need to examine the efficiency of current industry approaches. Factors such as mineralogical structure and inherent weakening in the form of micro cracks are known to affect ore breakage mechanisms. However, isolating and investigating individual factors under experimental conditions is challenging and typically impractical. Numerical techniques such as the Bonded Particle Model-Discrete Element Method (BPM-DEM) have been developed as a means of investigating in isolation, the effects of different factors on ore breakage behaviour under closely controlled breakage conditions. In this work, the robustness of the BPM-DEM in predicting fracture characteristics during SILC impact breakage is evaluated. Thereafter, the BPM-DEM is used to analyse the internal mechanical response of a simulated rock specimen under impact loading commensurate with that of the SILC. The method is shown to be an insightful opportunity to study intrinsic and extrinsic rock properties during dynamic loading and breakage

  Abstract
  In mineral processing, ore fracture is an essential first step for which the objective is to increase the exposed surface area of the valuable mineral, thereby increasing [...]

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• Effect of particle-size-scaling on particle interactions in DEM-simulations of sand in the context of air pluviation

  N. Heim, S. Henke

  WCCM2024.

  
  

  Abstract

  DEM (discrete element method) is a widely used numerical simulation method, which models the behaviour of a bulk substrate based on the individual interactions of many particles. One of its possible applications is the modelling of sand behaviour in different laboratory tests, e.g., cone penetration tests [1] or direct shear tests [2]. Furthermore, DEM is specifically of interest as a modelling method for investigating air pluviation, because it models the individual inter-particle and particle-environment interactions, both friction and collisions, which determine the compaction and homogeneity of the created samples. However, one disadvantage of DEM is the relatively long computational time [3] especially with decreasing particle sizes. This makes larger particle sizes compared to reality more interesting, especially for large scale or repeating simulations. On the other hand, if the size of the chosen particles is too large, certain interactions, such as interactions with other materials and equipment, may not be simulated in a way that properly represents real behaviour. This would lead to preferring smaller sized particles, which again would lead to longer computational times. Therefore, the chosen particle size as an important aspect of DEM simulations will be discussed, as well as the effects on different simulation aspects. This includes necessary parameter calibrations, the resulting inter-particle and particle-environment interactions as well as the achieved simulation results and accuracies. Of specific interest is the largest particle size, at which accurate and realistic results concerning real-world particle interactions can be achieved. Further, the effects of graded particle sizes to better represent the sand during the pluviation process will be discussed.

  Abstract
  DEM (discrete element method) is a widely used numerical simulation method, which models the behaviour of a bulk substrate based on the individual interactions of many particles. [...]

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• Full waveform modeling in seismic exploration based on a digital geological model using spectral element method on GPU

  A. Vershinin, A. Yury, V. Levin, K. Petrovsky

  WCCM2024.

  
  

  Abstract

  The paper considers the solution of a three-dimensional problem of modeling of all types of seismic waves propagating in real geological media. The numerical algorithm based on the spectral element method (SEM). The main advantages of SEM (high order space discretization, explicit time integration scheme) are presented in comparison with the classical approach based on the finite element method (FEM). The features of the massively parallel implementation of the algorithm on modern MultiGPU systems (based on A100 GPU) using CUDA technology are considered. The efficiency of parallelization on hybrid systems with different SEM orders and parameters of the numerical time integration scheme is analyzed. The results of solving a three-dimensional problem of modeling the propagation of seismic waves in a heterogeneous geological media with faults and sharply varying properties of layers are presented. Analysis of the numerical convergence of SEM for dispersive waves of the Rayleigh type is performed. Local and non-local non-reflective boundary conditions on the artificial boundary of the computational region are considered. The 3D computational model is constructed using a detailed digital geological model built for one of the Arctic regions. It was converted to an unstructured hexahedral mesh to perform SEM calculations using CAE FIDESYS software. The model is further generalized for typical seismic-geological conditions of Western Siberia, so that on the basis of such modeling it is possible to conduct a wide range of studies on the possibilities of seismic exploration to study the main oil and gas reservoirs in this region. The solution was sought on a hexahedral mesh consisting of 5.5 mln spectral elements of the 5th order with a total number of SEM nodes 1.2 billion. The output results of full-wave modeling are stored in the SEG-Y format, suitable for all types of industrial seismic processing. The analysis of the obtained model seismograms and wave fields is carried out. The conclusion is made about the practical significance of the conducted research.

  Abstract
  The paper considers the solution of a three-dimensional problem of modeling of all types of seismic waves propagating in real geological media. The numerical algorithm based [...]

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• The method of boundary integral equations in the boundary value problems of dynamics of fluids and gases

  Y. Krashanytsia

  WCCM2024.

  
  

  Abstract

  Based on the created generalized apparatus of vector-tensor analysis, integral representations of the main dynamic and kinematic characteristics of the problem of viscous gas flow around force systems of arbitrary spatial shape are constructed. The boundary value problem of the interaction of such systems with a viscous gas flow is reduced to a system of linear, conditioned by physical boundary conditions, boundary integral equations regarding the kinematic and dynamic characteristics of the problem. It is proven that all the obtained characteristics depend on the newly obtained irrotational vector potential of the momentum, which significantly simplifies the integral representations of solutions and their numerical implementation. On the basis of the created generalized apparatus of vector-tensor analysis, integral representations of the main dynamic and kinematic characteristics of the problem of the flow of a viscous gas flow around supporting systems of satisfactory spatial form have been constructed. The boundary value problem of the interaction of such systems with a viscous gas flow is reduced to a system of linear, conditioned by physical boundary conditions, boundary integral equations regarding the kinematic and dynamic characteristics of the problem. It is proven that all the obtained characteristics depend on the newly obtained, vortex-free vector potential of the momentum, which significantly simplifies the integral representations of the solutions and their numerical implementation.

  Abstract
  Based on the created generalized apparatus of vector-tensor analysis, integral representations of the main dynamic and kinematic characteristics of the problem of viscous [...]

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• Landslide run-out simulations with depth-averaged models and integration with 3D impact analysis using the Material Point Method

  M. Fois, A. Makarim, C. FALCO, A. Larese, L. Formaggia

  WCCM2024.

  
  

  Abstract

  Landslides pose a significant threat to human safety and the well-being of communities, making them one of the most challenging natural phenomena. Their potential for catastrophic consequences, both in terms of human lives and economic impact, is a major concern. Additionally, their inherent unpredictability adds to the complexity of managing the risks associated with landslides. It is crucial to continuously monitor areas susceptible to landslides. In situ detection systems like piezometers and strain gauges play a vital role in accurately monitoring internal pressures and surface movements in the targeted areas. Simultaneously, satellite surveys contribute by offering detailed topographic and elevation data for the study area. However, relying solely on empirical monitoring is insufficient for ensuring effective management of hazardous situations, especially in terms of preventive measures. This study provides advanced simulations of mudflows and fast landslides using particle depth-averaged methods, specifically employing the Material Point Method adapted for shallow water (Depth Averaged Material Point Method). The numerical method has been parallelized and validated through benchmark tests and real-world cases. Furthermore, the investigation extends to coupling the depth-averaged formulation with a three-dimensional one in order to have a detailed description of the impact phase of the sliding material on barriers and membranes. The multidimensional approach and its validation on real cases provide a robust foundation for a more profound and accurate understanding of the behavior of mudflows and fast landslides

  Abstract
  Landslides pose a significant threat to human safety and the well-being of communities, making them one of the most challenging natural phenomena. Their potential for catastrophic [...]

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