Central-upwind schemes for the Saint-Venant system
ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 3, pp. 397-425.

We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central schemes for systems of hyperbolic conservation laws to balance laws. Special attention is paid to the discretization of the source term such as to preserve stationary steady-state solutions. We also prove that the second-order version of our schemes preserves the nonnegativity of the height of the water. This important feature allows one to compute solutions for problems that include dry areas.

DOI : 10.1051/m2an:2002019
Classification : 65M06, 35L65
Mots-clés : Saint-Venant system, shallow water equations, high-order central-upwind schemes, balance laws, conservation laws, source terms 
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Kurganov, Alexander; Levy, Doron. Central-upwind schemes for the Saint-Venant system. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 3, pp. 397-425. doi : 10.1051/m2an:2002019. http://www.numdam.org/articles/10.1051/m2an:2002019/

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