The structure of well-balanced schemes for Friedrichs systems with linear relaxationReport as inadecuate

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1 LJLL - Laboratoire Jacques-Louis Lions 2 DSSI - Département des Sciences de la Simulation et de l-Information

Abstract : We study the conservative structure of linear Friedrichs systems with linear relaxation in view of the definition of well-balanced schemes. We introduce a particular global change of basis and show that the change-of-basis matrix can be used to develop a systematic treatment of well-balanced schemes in one dimension. This algebra sheds new light on a family of schemes proposed recently by L. Gosse 14. The application to the S n model a paradigm for the approximation of kinetic equations for radiation is detailed. The discussion of the singular case is performed, and the 2D extension is shown to be equal to a specific multidimensional scheme proposed in 5. This work is dedicated to the 2014 celebration of C. D. Munz- scientific accomplishments in the development of numerical methods for various problems in fluid mechanics.

Résumé : On étudie la structure des schémas bien équilibrés pour les systèmes de Friedrichs avec relaxation linéaire, avec application aux modèles Sn.

Keywords : well balanced schemes Friedrichs systems conservative formulation 65N99 65N06 finite volume schemes 2000 MSC: 65J10

Author: Bruno Després - Christophe Buet -



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