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Comptes Rendus Mathématique
Volume 349, n° 19-20
pages 1111-1115 (novembre 2011)
Doi : 10.1016/j.crma.2011.09.011
Received : 8 May 2011 ;  accepted : 15 September 2011
Spectral stability of finite volume schemes for linear hyperbolic systems
Stabilité spectrale des schémas volumes finis pour les systèmes hyperboliques linéaires
 

Michaël Ndjinga
Commissariat à lʼénergie atomique, centre de Saclay, DEN, DM2S, SFME, 91191 Gif-sur-Yvette, France 

Abstract

In this Note we prove the spectral stability of a large class of finite volume schemes applied to hyperbolic systems of linear partial differential equations on multidimensional unstructured meshes. This class requires that the upwinding matrix has positive eigenvalues and is codiagonalisable with the system matrices. That includes among others the upwind and centred implicit schemes, and the upwind explicit scheme under a CFL condition.

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Résumé

Dans cette Note nous démontrons la stabilité spectrale dʼune grande classe de schémas volumes finis pour la résolution des systèmes hyperboliques dʼéquations aux dérivées partielles linéaires sur maillages non structurés. Cette classe requiert que la matrice de décentrement ait des valeurs propres positives et soit codiagonalisable avec les matrices du système. Elle inclut notament les schémas centré et décentré amont implicites, et le schéma décentré amont explicite sous une condition CFL.

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