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Generalized Harten Formalism and Longitudinal Variation Diminishing schemes for Linear Advection on Arbitrary Grids

Published online by Cambridge University Press:  15 April 2002

Bruno Després  and
Frédéric Lagoutière
Bruno Després
Affiliation:
Commissariat à l'Énergie Atomique, BP 12, 91680 Bruyères-le-Châtel, France. (Bruno.Despres@cea.fr) Laboratoire d'analyse numérique, Université de Paris VI, 175 rue du Chevaleret, 75013 Paris, France. (despres@ann.jussieu.fr)
Frédéric Lagoutière
Affiliation:
Laboratoire d'analyse numérique, Université de Paris VI, 175 rue du Chevaleret, 75013 Paris, France. (despres@ann.jussieu.fr)
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Abstract

We study a family of non linear schemes for the numerical solution of linear advection on arbitrary grids in several space dimension. A proof of weak convergence of the family of schemes is given, based on a new Longitudinal Variation Diminishing (LVD) estimate. This estimate is a multidimensional equivalent to the well-known TVD estimate in one dimension. The proof uses a corollary of the Perron-Frobenius theorem applied to a generalized Harten formalism.

Keywords

LVD estimateHarten Formalismlinear advectionfinite volume methods.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 6 , November 2001 , pp. 1159 - 1183
Copyright
© EDP Sciences, SMAI, 2001

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