Skip to Main content Skip to Navigation
Journal articles

Finite Volume Schemes on Unstructured Grids for Non-Local Models: Application to the Simulation of Heat Transport in Plasmas

Thierry Goudon 1, 2 Martin Parisot 3
1 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
3 SIMPAF - SImulations and Modeling for PArticles and Fluids
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : In the so-called Spitzer-Harm regime, equations of plasma physics reduce to a non linear parabolic equation for the electronic temperature. Coming back to the derivation of this limiting equation through hydrodynamic regime arguments, one is led to construct a hierarchy of models where the heat fluxes are defined through a non-local relation which can be reinterpreted as well by introducing coupled diffusion equations. We address the question of designing numerical methods to simulate these equations. The basic requirement for the scheme is to be asymptotically consistent with the Spitzer-Harm regime. Furthermore, the constraints of physically realistic simulations make the use of unstructured meshes un-avoidable. We develop a Finite Volume scheme, based on Vertex-Based discretization, which reaches these objectives. We discuss on numerical grounds the efficiency of the method, and the ability of the generalized models in capturing relevant phenomena missed by the asymptotic problem.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01089051
Contributor : Martin Parisot <>
Submitted on : Monday, December 1, 2014 - 8:59:55 AM
Last modification on : Friday, November 27, 2020 - 2:18:02 PM

Identifiers

Citation

Thierry Goudon, Martin Parisot. Finite Volume Schemes on Unstructured Grids for Non-Local Models: Application to the Simulation of Heat Transport in Plasmas. Journal of Computational Physics, Elsevier, 2012, 231, pp.20. ⟨10.1016/j.jcp.2012.07.050⟩. ⟨hal-01089051⟩

Share

Metrics

Record views

361