engleski

Numerical Modelling of Free-Surface Flows with Variable Bottom Topography

This paper presents possible ways of dealing with the problem of correct handling the source term in the case when finite difference upwind method based on approximate Poe's Riemann solver has been applied for the numerical solution of the one- dimensional free-surface flow with variable bottom topography. The possibilitiy of writing the continuity equation in two different ways, with water depth or with water surface elevation as dependent variables, has been considered. These two variations were combined with two approaches of discretizing the source term: centered discretization of the source term and upwinding of the source term in tne same manner as the physical flux. Numerical results on the test case that simulates the propagation of the tidal wave in the channel with variable bottom topography shows that the upwinding of the source term can be avoided if the surface elevation is used as dependent variable in the continuity equation.

free-surface flow ; source term ; centered discretization ; upwinding

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