A well-balanced numerical scheme for shallow-water equations with topography : resonance phenomena

Abstract :

The shallow water model with a source term due to topography gradient is approximated within the frame of Finite Volume numerical methods. The cornerstone of the method is the solution of the inhomogeneous Riemann problem. Thus the numerical scheme can deal simultaneously with discrete steady states, flood, occurrence and covering of dry zones.

We present the parameterization through the discontinuity of topography, emphasizing on the resonance phenomenon. We then build the solution of the inhomogeneous Riemann problem using a continuation method with respect to the jump of topography. Finally, numerical experiments illustrate the agreement of the numerical method with the previous analysis.

Date of publication: April 2004

Paper presented by : Professor Jean-Marc Herard