STABILITY, ACCURACY AND EFFICIENCY OF A SEMIIMPLICIT METHOD FOR 3-DIMENSIONAL SHALLOW-WATER FLOW

The stability analysis, the accuracy and the efficiency of a semi-impl icit finite difference scheme for the numerical solution of a three-di mensional shallow water model are presented and discussed. The governi ng equations are the three-dimensional Reynolds equations in which pre ssure is assumed to be hydrostatic. The pressure gradient in the momen tum equations and the velocities in the vertically integrated continui ty equation are discretized with the theta-method, with theta being an implicitness parameter. It is shown that the method is stable for 1/2 less than or equal to theta less than or equal to 1, unstable for the ta < 1/2 and highest accuracy and efficiency is achieved when theta = 1/2 The resulting algorithm is mass conservative and naturally allows for the simulation of flooding and drying of tidal flats.