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Journal of Scientific Computing

, Volume 30, Issue 1, pp 131–175 | Cite as

Residual Distribution Schemes on Quadrilateral Meshes

  • R. Abgrall
  • F. Marpeau
Article

Abstract

We propose an investigation of the residual distribution schemes for the numerical approximation of two-dimensional hyperbolic systems of conservation laws on general quadrilateral meshes. In comparison to the use of triangular cells, usual basic features are recovered, an extension of the upwinding concept is given, and a Lax–Wendroff type theorem is adapted for consistency. We show how to retrieve many variants of standard first and second-order accurate schemes. They are proven to satisfy this theorem. An important part of this paper is devoted to the validation of these schemes by various numerical tests for scalar equations and the Euler equations system for compressible fluid dynamics on non Cartesian grids. In particular, second-order accuracy is reached by an adaptation of the Linearity preserving property to quadrangle meshes. We discuss several choices as well as the convergence of iterative method to steady state. We also provide examples of schemes that are not constructed from an upwinding principle

Keywords

Conservation laws residual distribution schemes structured and hybrid meshes non oscillatory schemes 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Mathématiques Appliquées de BordeauxUniversité Bordeaux 1Talence CedexFrance
  2. 2.Institut Universitaire de France and Projet ScalapplixINRIA FutURsParisFrance

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