Some approximate Godunov schemes to compute shallow-water equations with topographyReportar como inadecuado

Some approximate Godunov schemes to compute shallow-water equations with topography - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

1 I2M - Institut de Mathématiques de Marseille 2 EDF R&D - EDF Recherche et Développement 3 ANGE - Numerical Analysis, Geophysics and Ecology LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt 4 LJLL - Laboratoire Jacques-Louis Lions

Abstract : We study here the computation of shallow-water equations with topography by Finite Volume methods, in a one-dimensional framework though all methods introduced may be naturally extended in two dimensions. All methods performed are based on a dicretisation of the topography by a piecewise function constant on each cell of the mesh, from an original idea of A.Y. Le Roux et al

Whereas the Well-Balanced scheme of A.Y. Le Roux is based on the exact resolution of each Riemann problem, we consider here approximate Riemann solvers, namely the VFRoencv schemes. Several single step methods are derived from this formalism, and numerical results are compared to a fractional step method. Some tests cases are presented : convergence to steady states in subcritical and supercritical conngurations, occurence of dry area by a drain over a bump and occurence of vacuum by a double rarefaction wave over a step. Numerical schemes, combined with an appropriate high order extension, provide accurate and convergent approximations.

Autor: Thierry Gallouet - Jean-Marc Hérard - Nicolas Seguin -



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