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A Discontinuous Galerkin semi-Lagrangian solver for the guiding-center problem

Nicolas Crouseilles 1, 2 Michel Mehrenberger 3, 4 Francesco Vecil 5
2 IPSO - Invariant Preserving SOlvers
Inria Rennes – Bretagne Atlantique , IRMAR - Institut de Recherche Mathématique de Rennes
3 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : In this paper, we test an innovative numerical scheme for the simulation of the guiding-center model, of interest in the domain of plasma physics, namely for fusion devices. We propose a 1D Discontinuous Galerkin (DG) discretization, whose basis are the Lagrange polynomials interpolating the Gauss points inside each cell, coupled to a conservative semi-Lagrangian (SL) strategy. Then, we pass to the 2D setting by means of a second-order Strangsplitting strategy. In order to solve the 2D Poisson equation on the DG discretization, we adapt the spectral strategy used for equally-spaced meshes to our Gauss-point-based basis. The 1D solver is validated on a standard benchmark for the nonlinear advection; then, the 2D solver is tested against the swirling deformation ow test case; nally, we pass to the simulation of the guiding-center model, and compare our numerical results to those given by the Backward Semi-Lagrangian method.
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https://hal.inria.fr/hal-00717155
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Submitted on : Thursday, July 12, 2012 - 9:54:21 AM
Last modification on : Monday, July 6, 2020 - 3:38:10 PM
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  • HAL Id : hal-00717155, version 1

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Nicolas Crouseilles, Michel Mehrenberger, Francesco Vecil. A Discontinuous Galerkin semi-Lagrangian solver for the guiding-center problem. 2012. ⟨hal-00717155⟩

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