Un schéma TVD-multirésolution pour les équations de Saint-Venant

A high-resolution algorithm is proposed for the solution of the two-dimensional shallow-water equations by adopting the numerical flux for the generalized formulation of the TVD scheme developed by Harten and Yee. In order to reduce the number of numerical flux computations in the shallow water equations, the multiresolution approach is proposed. The method is based on the analysis of the solution's regularity according to various levels of resolution. This technique provides a very useful tool for removing superfluous calculation where the solution is over resolved. Numerical tests are conducted in order to evaluate the performance of the method. The presented results show efficiency of the multiresolution algorithm and reduction in CPU time. A variety of hydraulic test cases is presented to assess the validity and the performance of the method.