This thesis is a contribution to the numerical solution of a hyperbolic conservation law resulting from a coupling between the Saint-Venant equations, for the modeling of flows in shallow water, and transport-diffusion equation of a non active pollutant. The mathematical model used is two dimensional, incorporating terms of friction, diffusion, surface tension and a term of variation of the bathymetry. We present a numerical model based on a higher order two-dimensional finite volume scheme , conservative and consistent, on an adaptive unstructured mesh , this model preserves the positivity of water depth and the steady state associated with the lake at rest, it can accurately capture shock waves. In a time extension to the second order is guaranteed by using a Runge-Kutta which will take into account the different speeds of propagation of information in the different issues involved. We apply the numerical model developed over several issues. Among other things, the simulation of propagation of a flood wave, flow around a singularity geometric flow on variable funds and having steep edges. And in the end, the numerical study ends with an application of the model for the simulation of pollutant transport in a real geometry with a highly variable bathymetry as like the bay of Tangier.