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1 Department of Applied Mathematics Heraklion 2 ICS-FORTH - Institute of Computer Science Crete 3 DMA - Département de Mathématiques et Applications 4 PDEs and Numerical Analysis DMA - Département de Mathématiques et Applications, ICS-FORTH - Institute of Computer Science Crete

Abstract : Hyperbolic conservation laws with source terms arise in many applications, especially as a model for geophysical flows because of the gravity, and their numerical approximation leads to specific difficulties. In the context of finite volume schemes, many authors have proposed to Upwind Sources at Interfaces, i.e. the U.S.I. method, while a cell-centered treatment seems more natural. This note gives a general mathematical formalism for such schemes. We define consistency and give a stability condition for the U.S.I. method. We relate the notion of consistency to the -well-balanced- property, but its stability remains open, and we also study second order approximations as well as error estimates. The general case of a nonuniform spatial mesh is particularly interesting, motivated by two dimensional problems set on unstructured grids.

Keywords : second-order approximations conservation laws upwinding source terms finite volume schemes error estimates second-order approximations.





Autor: Theodoros Katsaounis - Benoît Perthame - Chiara Simeoni -

Fuente: https://hal.archives-ouvertes.fr/



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