PREDICTION METHOD FOR SHALLOW WATER EQUATIONS BASED ON THE METHOD FOR INCOMPRESSIBLE FLUIDS WITH COLLOCATED GRID

This paper presents a computational method for shallow water equations on the basis of the prediction method proposed for incompressible Navier-Stokes equations on a collocated grid system. In the proposed method, the momentum equations are discretized with a semi-implicit method with respect to the water depth, h. The continuity equation is discretized implicitly and its numerical solutions are obtained by solving simultaneous equations. The unit flow rates, M and N, are corrected with the converged results for h. It has been shown that the proposed method is numerically stable and that higher-order schemes for convection terms, C-HSMAC and C-ISMAC methods, which have been proposed for the computations of incompressible flows, are available for shallow water equations as well.