Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids

Després, Bruno; Lagoutière, Frédéric

Després, Bruno ; Lagoutière, Frédéric

ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 6, pp. 1159-1183.

Résumé
Abstract

Nous étudions une famille de schémas non linéaires pour l'approximation numérique de l'advection linéaire sur grille quelconque en dimension d'espace supérieure à un. Une preuve de convergence est proposée à partir d'une estimation de la variation longitudinale. Cette estimation est une généralisation multidimensionnelle discrète de l'estimation TVD discrète, bien connue en dimension un d'espace.

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.

MR Zbl

Classification : 76M12, 65M12
Mots clés : LVD estimate, Harten formalism, linear advection, finite volume methods

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     author = {Despr\'es, Bruno and Lagouti\`ere, Fr\'ed\'eric},
     title = {Generalized {Harten} formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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Després, Bruno; Lagoutière, Frédéric. Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 6, pp. 1159-1183. http://www.numdam.org/item/M2AN_2001__35_6_1159_0/

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