Title: Well-balanced scheme for shallow water equations with arbitrary topography

Authors: Mai Duc Thanh, Md. Fazlul Karim, Ahmad Izani Md. Ismail

Addresses: Department of Mathematics, International University, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam. ' School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia. ' School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia

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.

Keywords: shallow water equations; conservation law; well-balanced scheme; arbitrary topography; stationary waves.

DOI: 10.1504/IJDSDE.2008.019681

International Journal of Dynamical Systems and Differential Equations, 2008 Vol.1 No.3, pp.196 - 204

Published online: 20 Jul 2008 *

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