WIT Press

A Finite Volume Model For The Resolution Of The Shallow Water Equations With Moving Boundary Conditions


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WIT Press


J. Fe, F. Navarrina & J. Puertas


A numerical model for the two dimensional ShallowWater Equations is described and tested. The Finite Volume Method is applied, upwinding the flux and geometric source terms, but not the friction term. The performance of the model in different situations is shown, including the advance of a shock over an horizontal dry bed and the simulation of an hydraulic jump. The results confirm the good behaviour of the model. Keywords: shallow water equations, free surface flows, dry bed. 1 Introduction The Navier–Stokes Equations (NSE) are a non linear hyperbolic system of conservation laws, that controls the behaviour of viscous fluids in three dimensions. In many flows, such as estuaries or wide channels, the horizontal dimensions are predominant. If the vertical variation of the horizontal components of the velocity is small and the vertical acceleration is negligible, then the flow can be properly described by the two-dimensional Shallow Water Equations. SWE can be solved through first-order schemes, easy to implement, and it is rather common the upwinding of the flux term of the equations to stabilize the model and give more importance to the side from which the information comes. The work is distributed as follows: in section 2 the obtaining of the SWE is summarized and the hypothesis used in it are enumerate. In section 3 the applying of the Finite Volume Method (FVM) to the equations is described and, in section 4, some examples of validation–involving different boundary conditions– are shown.


shallow water equations, free surface flows, dry bed.