A 2D finte volume scheme for hybrid unstructured grids

A 2D numerical scheme to solve the shallow water equations is presented. The equations are solved in time by means of a Strang splitting approach. Exploiting the rotational invariance, the advective part of the problem is evaluated solving at first order a sequence of augmented 1D Riemann problems. The scheme works on unstructured triangular and quadrangular elements, also mixed together. Thus the domain can be discretized in the best possible way, following the main flow direction with quadrangular almost regular cells and maintaining quite homogeneous grid sizes. The former characteristic allows the scheme to work more effectively along the main flow direction and the latter helps in reducing computational time. The model can be easily applied to real environmental problems, with complex topography. The numerical scheme is applied to 1D and 2D dam break problem with good results. Different grids are used to check the influence of the domain discretization on the results.