Well-balanced scheme for shallow water equations with arbitrary topography (Q960314)

Summary: We study one-dimensional shallow water equations with arbitrary topography. We first verify that traditional discretizations of the right-hand side of the equation of balance of momentum give unsatisfactory results. We then show that the equations can be written in divergence form for stationary waves. Motivated by the encouraging results for the well-balanced scheme for fluid flows in a nozzle with variable cross-section in \textit{D. Kröner} and \textit{M. D. Thanh} [SIAM J. Numer. Anal. 43, No.~2, 796--824 (2005; Zbl 1093.35050)], we construct a numerical scheme based on stationary waves. This scheme is constructed so that it maintains equilibrium states. Tests show that our scheme is both stable and fast.