High-order dimensionally split Lagrange-remap schemes for ideal magnetohydrodynamics

Marc Wolff; Stéphane Jaouen; Hervé Jourdren; Eric Sonnendrücker

doi:10.3934/dcdss.2012.5.345

Article Contents

2012, Volume 5, Issue 2: 345-367. Doi: 10.3934/dcdss.2012.5.345

This issue Previous Article Models and simulations for the laser-plasma interaction and the three-wave coupling problem Next Article

High-order dimensionally split Lagrange-remap schemes for ideal magnetohydrodynamics

1.
CEA, DAM, DIF, F-91297 Arpajon
2.
INRIA Nancy-Grand Est, 615 rue du Jardin Botanique, 54600 Villers-lès-Nancy, IRMA, Université de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg Cedex

Received: June 30, 2009

Revised: January 31, 2010

Published: March 2012

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Abstract

We first propose a new class of high-order finite volume schemes for solving the 1-D ideal magnetohydrodynamics equations that is particularly well-suited for modern computer architectures. Applicable to arbitrary equations of state, these schemes, based on a Lagrange-remap approach, are high-order accurate in both space and time in the non-linear regime. A multidimensional extension on 2-D Cartesian grids using a high-order dimensional splitting technique is then proposed. Numerical results up to fourth-order on smooth and non-smooth test problems are also provided.

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Mathematics Subject Classification: Primary: 35L75, 76W05; Secondary: 35L65.

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