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Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)

Published online by Cambridge University Press:  20 January 2014

Christophe Berthon ,
Yves Coudière  and
Vivien Desveaux
Christophe Berthon
Affiliation:
Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France.. vivien.desveaux@univ-nantes.fr
Yves Coudière
Affiliation:
Institut de Mathématiques de Bordeaux, CNRS UMR 5251, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France. INRIA Sud-Ouest, 351 cours de la Libération, 33405 Talence Cedex, France.
Vivien Desveaux
Affiliation:
Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France.. vivien.desveaux@univ-nantes.fr
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Abstract

We discuss new MUSCL reconstructions to approximate the solutions of hyperbolic systems of conservations laws on 2D unstructured meshes. To address such an issue, we write two MUSCL schemes on two overlapping meshes. A gradient reconstruction procedure is next defined by involving both approximations coming from each MUSCL scheme. This process increases the number of numerical unknowns, but it allows to reconstruct very accurate gradients. Moreover a particular attention is paid on the limitation procedure to enforce the required robustness property. Indeed, the invariant region is usually preserved at the expense of a more restrictive CFL condition. Here, we try to optimize this condition in order to reduce the computational cost.

Keywords

Systems of conservation lawsMUSCL methodunstructured meshesdual meshinvariant region
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 2: Multiscale problems and techniques , March 2014 , pp. 583 - 602
Copyright
© EDP Sciences, SMAI, 2014

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