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Preprint 2015-021

Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system

Emmanuel Audusse, François Bouchut, Marie-Odile Bristeau and Jacques Sainte-Marie

Abstract: A lot of well-balanced schemes have been proposed for discretizing the classical Saint-Venant system for shallow water flows with non-flat bottom. Among them, the hydrostatic reconstruction scheme is a simple and efficient one. It involves the knowledge of an arbitrary solver for the homogeneous problem (for example Godunov, Roe, kinetic …). If this solver is entropy satisfying, then the hydrostatic reconstruction scheme satisfies a semi-discrete entropy inequality. In this paper we prove that, when used with the classical kinetic solver, the hydrostatic reconstruction scheme also satisfies a fully discrete entropy inequality, but with an error term. This error term tends to zero strongly when the space step tends to zero, including solutions with shocks. We prove also that the hydrostatic reconstruction scheme does not satisfy the entropy inequality without error term.

Paper:
Available as PDF (220 Kbytes).
Author(s):
Emmanuel Audusse
François Bouchut
Marie-Odile Bristeau
Jacques Sainte-Marie
Publishing information:
To appear in Mathematics of Computation
Submitted by:
; 2015-07-27.