A Two-Dimensional Numerical Model for Shallow Water Flows over Variable Topographies

Based on well-balanced Roe’s approximate Riemann solver, a numerical model is developed for the unsteady, two-dimensional, shallow water flow with variable topographies. In this model, an efficient methods are applied to treat the source terms and to satisfy the compatibility condition on unstructured grids. In the method, different components of the bed slope source term are considered separately and the compatible discretization of the components is presented. The newly developed model is verified against analytical solutions and measured date, with good agreement.