Coupling techniques for nonlinear hyperbolic equations. IV. Well-balanced schemes for scalar multi-dimensional and multi-component laws - Laboratoire Jacques-Louis Lions Accéder directement au contenu
Article Dans Une Revue Mathematics of Computation Année : 2015

Coupling techniques for nonlinear hyperbolic equations. IV. Well-balanced schemes for scalar multi-dimensional and multi-component laws

Résumé

This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of partial differential equations. In an earlier work, this strategy allowed us to develop a regularization method based on a thick interface model in one space variable for coupling scalar equations. In the present paper, we significantly extend this framework and, in addition, encompass equations in several space variables. This new formulation includes the coupling of several distinct scalar conservation laws and allows for a possible covering in space. Our main contributions are, on one hand, the design and analysis of a well–balanced finite volume method on general triangulations and, on the other hand, a proof of convergence of this method toward entropy solutions, extending Coquel, Cockburn, and LeFloch's theory (restricted to a single conservation law without coupling). The core of our analysis is, first, the derivation of entropy inequalities as well as a discrete entropy dissipation estimate and, second, a proof of convergence toward the entropy solution of the coupling problem.
Fichier principal
Vignette du fichier
BCL-Part4-revised.pdf (677.99 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00703885 , version 1 (28-04-2015)

Identifiants

Citer

Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch. Coupling techniques for nonlinear hyperbolic equations. IV. Well-balanced schemes for scalar multi-dimensional and multi-component laws. Mathematics of Computation, 2015, 84 (294), pp.1663-1702. ⟨10.1090/S0025-5718-2015-02933-0⟩. ⟨hal-00703885⟩
326 Consultations
159 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More