A Numerical Simulation of the Shallow Water Flow on a Complex Topography

In current chapter, we have thoroughly described a numerical integration scheme of nonstationary 2D equations of shallow water. The scheme combines the smoothed particle hydrodynamics (SPH) and the total variation diminishing (TVD) methods, which are sequentially used at various steps of the combined SPH-TVD algorithm. The method is conservative and well balanced. It provides stable through calculations in presence of nonstationary “water-dry bottom” boundaries on complex irregular bottom topography including the transition of such a boundary between wet and dry bottom through the computational boundary. Multifarious tests demonstrate the effectiveness of the combined SPH-TVD scheme application for a solution of diverse problems of the engineering hydrology.