Numerical Model for the Simulation of Two-Dimensional Shallow-Water Flows of Arbitrary Topography

A numerical model based on a second-order upwind finite volume method is developed for unsteady, two-dimensional, shallow-water flow over arbitrary topography with moving boundaries. The HLL approximate Riemann solver is used for the computation of inviscid flux functions, which makes it possible to handle discontinuous solutions. To prevent numerical truncation errors due to the pressure and bed slope terms from artificially accelerating quiescent water over an arbitrary bed, the classic HLL scheme is modified. In addition, a simple and efficient procedure is presented to simulate the movement of moving boundaries. The good quality of the results is illustrated by means of two shallow water flow test cases.