A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations

2015/02/25 by Christophe Berthon, Christophe Chalons · 2 citations
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions

paper · doi:10.1090/mcom3045

Abstract

This work is devoted to the derivation of a fully well-balanced numerical scheme for the well-known shallow-water model. During the last two decades, several well-balanced strategies have been introduced with special attention to the exact capture of the stationary states associated with the so-called lake at rest. By fully well-balanced, we mean here that the proposed Godunov-type method is also able to preserve stationary states with non zero velocity. The numerical procedure is shown to preserve the positiveness of the water height and satisfies a discrete entropy inequality.

Citations

• Hyperbolic systems of conservation laws II

Cited by

• Towards a fully well-balanced and entropy-stable scheme for the Euler equations with gravity: preserving isentropic steady solutions
• Asymptotic preserving schemes for hyperbolic systems with relaxation

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