Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method

Jan Sickmann Hesthaven
Global Science Press, 2015
Article

Discontinuous Galerkin (DG) and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical model- ing of magma dynamics in 2D and 3D using the library deal.II . The physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance and one elliptic equation to recover global pressure. A combination of a discontinuous Galerkin method for the advection equa- tions and a finite element method for the elliptic equation provide a robust and efficient solution to the channel regime problems of the physical system in 3D. A projective and adaptively applied pressure estimation is employed to significantly reduce the compu- tational wall time without impacting the overall physical reliability in the modeling of important features of melt and segregation, such as melt channel bifurcation in 2D and 3D time dependent simulations.

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Concepts associés

Chargement

Publications associées

Chargement

Jan Sickmann Hesthaven
Global Science Press, 2015
Article

Résumé

Official source

https://infoscience.epfl.ch/record/197481?ln=fr

À propos de ce résultat

Concepts associés (9)

Concepts associés

Chargement

Publications associées (3)

Chargement

Publications associées

Chargement

Méthode des éléments finis

En analyse numérique, la méthode des éléments finis (MEF, ou FEM pour finite element method en anglais) est utilisée pour résoudre numériquement des équations aux dérivées partielles. Celles-ci pe

Simulation de phénomènes

La simulation de phénomènes est un outil utilisé dans le domaine de la recherche et du développement. Elle permet d'étudier les réactions d'un système à différentes contraintes pour en déduire les r

Méthode des différences finies

En analyse numérique, la méthode des différences finies est une technique courante de recherche de solutions approchées d'équations aux dérivées partielles qui consiste à résoudre un système de relati

Numerical simulation of free surface flows

Vincent Maronnier, Marco Picasso, Jacques Rappaz

A numerical model is presented for the simulation of complex fluid flows with free surfaces. The unknowns are the velocity and pressure fields in the liquid region, together with a function defining the volume fraction of liquid. Although the mathematical formulation of the model is similar to the volume of fluid (VOF) method, the numerical schemes used to solve the problem are different. A splitting method is used for the time discretization. At each time step, two advection problems and a generalized Stokes problem are to be solved. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small rectangular cells, using a forward characteristic method. The generalized Stokes problem is solved using a finite element method on a fixed, unstructured mesh. Numerical results are presented for several test cases: the filling of an S-shaped channel, the filling of a disk with core, the broken dam in a confined domain. (C) 1999 Academic Press.

1999

Chargement

A meshless method to simulate interactions between large soft tissue and a surgical grasper

Elahe Abdi

Realistic simulation of tool-tissue interactions can help to develop more effective surgical training systems and simulators. This study uses a finite element and meshless modeling approach to simulate the grasping procedure of a large intra-abdominal organ, i.e. a kidney, during laparoscopic surgery. Results indicate that the accuracy of the meshless method is comparable with that of the finite element method, with root mean square errors in the range of 0.8 to 2.3 mm in different directions. For the model presented in this study, the computational cost of the meshless method was much less than that of the finite element model. (C) 2016 Sharif University of Technology. All rights reserved.

Elsevier Science Bv2016

Chargement

Numerical simulation of sediment dynamics with free surface flows

Arwa Mrad

We present a numerical model for the simulation of 3D mono-dispersed sediment dynamics in a Newtonian flow with free surfaces. The physical model is a macroscopic model for the transport of sediment based on a sediment concentration with a single momentum balance equation for the mixture (fluid and sediments). The model proposed here couples the Navier-Stokes equations, with a volume-of-fluid (VOF) approach for the tracking of the free surfaces between the liquid and the air, plus a nonlinear advection equation for the sediments (for the transport, deposition, and resuspension of sediments). The numerical algorithm relies on a splitting approach to decouple diffusion and advection phenomena such that we are left with a Stokes operator, an advection operator, and deposition/resuspension operators. For the space discretization, a two-grid method couples a finite element discretization for the resolution of the Stokes problem, and a finer structured grid of small cells for the discretization of the advection operator and the sediment deposition/resuspension operator. SLIC, redistribution, and decompression algorithms are used for post-processing to limit numerical diffusion and correct the numerical compression of the volume fraction of liquid. The numerical model is validated through numerical experiments. We validate and benchmark the model with deposition effects only for some specific experiments, in particular erosion experiments. Then, we validate and benchmark the model in which we introduce resuspension effects. After that, we discuss the limitations of the underlying physical models. Finally, we consider a one-dimensional diffusion-convection equation and study an error indicator for the design of adaptive algorithms. First, we consider a finite element backward scheme, and then, a splitting scheme that separates the diffusion and the convection parts of the equation.

EPFL2021

Chargement