A NEW IMPLICIT SCHEME FOR SOLVING 3-D SHALLOW WATER FLOWS

Based on the improved ADI method, this article proposes an improved implicit finite difference scheme for solving 3-D shallow water flows. The main objective is to design a numerical relation between the horizontal velocity on each layer and the depth-averaged velocity for employing the improved ADI method. With the free surface elevation and the depth-averaged velocity obtained by using essentially 2-D depth-averaged mode, the velocity profiles can be obtained easily and simultaneously. The wind-induced flows, the open channel flows due to the pressure gradient and the tidal flows in coastal waters are simulated, and the results are consistent well with the analytical solution and the field data, which shows that the present implicit scheme is stable and effective, and the established model is practical. Moreover, when only one vertical layer is specified, the present 3-D numerical model is reducea to the 2-D depth-averaged model.