Construction of second-order accurate monotone and stable residual distribution schemes for steady problems

Authors:
Rémi Abgrall;Mohamed Mezine
Affiliations:
Mathématiques Appliquées de Bordeaux, Université Bordeaux I, 351 cours de la Libération, 33 405 Talence Cedex, France;Mathématiques Appliquées de Bordeaux, Université Bordeaux I, 351 cours de la Libération, 33 405 Talence Cedex, France
Venue:
Journal of Computational Physics
Year:
2004

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Abstract

After having recalled the basic concepts of residual distribution (RD) schemes, we provide a systematic construction of distribution schemes able to handle general unstructured meshes, extending the work of Sidilkover. Then, by using the concept of simple waves, we show how to generalize this technique to symmetrizable linear systems. A stability analysis is provided. We formally extend this construction to the Euler equations. Several test cases are presented to validate our approach.