Semi-Lagrangian semi-implicit time-splitting scheme for the shallow water equations
Time-splitting technique applied in the context of the semi-Lagrangian semi-implicit method allows the use of extended time steps mainly based on physical considerations and reduces the number of numerical operations at each time step such that it is approximately proportional to the number of the points of spatial grid. To control time growth of the additional truncation errors, the standard stabilizing correction method is modified with no penalty for accuracy and efficiency of the algorithm. A linear analysis shows that constructed scheme is stable for time steps up to 2 h. Numerical integrations with actual atmospheric fields of pressure and wind confirm computational efficiency, extended stability and accuracy of the proposed scheme. Copyright (c) 2006 John Wiley & Sons, Ltd.
shallow water equations semi-lagrangian method time splitting