MPI-Based Simulation of the Shallow Water Model using the Finite Volume Characteristics Scheme

A parallel algorithm for solving the 2D shallow water equations coupled with the convection-diffusion equation has been developed, in order to demonstrate the capability and performance of our parallel approach while maintaining very good accuracy of the results obtained. The numerical scheme used is written in a non-uniform triangular grid formalism, which allows for the complexity of the geometry of the computational domain used. This approach is based on both predictor and corrector stages. The predictor one uses the method of characteristics to reconstruct the numerical fluxes, whereas the corrector stage recovers the conservation equations. Numerical results are presented for a pollutant transport in a squared cavity.