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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.

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