Properties of two computational methods for shallow water flow problems

Some properties of two computational methods for shallow water flow problems have passed in review. These methods are a composite ADI technique and a fully implicit splitting method. Both methods are unconditionally stable and have a fourth order dissipation. The ADI technique is very efficient and robust. Many important practical situations have been calculated successfully. The time step of this technique, however, is limited due to a restricted numerical domain of influence. The fully implicit time splitting method is able to use much larger time steps. It performs well in test problems. In the resolution of the arising linear systems, the quality of the solver determines to a large extent the costs of the method. At present a Conjugate Gradients Squared algorithm is implemented.