A FULLY WELL-BALANCED, POSITIVE AND ENTROPY-SATISFYING GODUNOV-TYPE METHOD FOR THE SHALLOW-WATER EQUATIONS

Christophe Berthon (1) , Christophe Chalons (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LMV - Laboratoire de Mathématiques de Versailles

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 a 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.

Mots clés: entropy preserving scheme; positive preserving scheme; well-balanced property; finite volume schemes; Shallow-water equations; steady states

Domaines: Analyse numérique [math.NA]

Christophe Berthon, Christophe Chalons. A FULLY WELL-BALANCED, POSITIVE AND ENTROPY-SATISFYING GODUNOV-TYPE METHOD FOR THE SHALLOW-WATER EQUATIONS. Mathematics of Computation, 2016, 85 (299), pp.1281-1307. ⟨hal-00956799v2⟩