A Simple Well-balanced Scheme for Shallow Water Flows Over Irregular Beds with Wet/Dry Front

A well-balanced numerical scheme has been established to simulate 1-D shallow water flow over irregular bottom topography with wetting and drying. The flux term is calculated by the approximate Riemann solver of Roe, which can capture discontinuities and shocks. And Monotonic Upstream–Centered Scheme for Conservation Laws (MUSCL scheme) is used to reconstruct the data. To preserve stationary conditions (the so called c-property), the surface gradient method, together with the definition of bed elevation at the cell boundaries, is employed to keep the water surface constant. Also, to balance the numerical flux term, the discretization of the bed slope source term has been modified, with the water depth written as the average of four reconstructed water depths appearing in the numerical flux term. To track wet/dry front efficiently, data reconstruction method, interface flux calculation and transition between water depth and water level are adjusted. The satisfactory performance of the modified balanced Roe-MUSCL scheme in a series of numerical tests indicates that the scheme is robust and effective.