Well-balanced scheme for shallow water equations with arbitrary topography
by Mai Duc Thanh, Md. Fazlul Karim, Ahmad Izani Md. Ismail
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 1, No. 3, 2008

Abstract: We study the one-dimensional shallow water equations with arbitrary topography. We first verify that traditional discretisations of the right-hand side of the equation of the balance of momentum give unsatisfactory results. We then show that the equations can be written in the 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 Kroner and Thanh (2005), 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.

Online publication date: Sun, 20-Jul-2008

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