On numerical treatment of shallow water flow over the dry bed including balancing

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Abstract

The shallow water equations are accepted in many practical applications as the governing equations for the unsteady water flow in natural watercourses and in the case of flooding. For modelling a realistic problem it is necessary to use this nonhomogeneous system that includes source terms relevant to the varying bed topography. The first emphasis of this work is on using the numerical scheme in which the source term is appropriately discretized, so that the balance between the flux gradient and the source term is obtained. The first order scheme developed by Hubbard and Garcia-Navarro in [5] by an extension of the standard upwind finite volume numerical scheme based on the Roe’ s approximate solver, satisfies that balancing property, so we present it and use it in this work. The scheme is applied here to both one- and two-dimensional problems. Besides the problem of the correct source term discretisati

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