ACCURACY AND STABILITY OF FINITE DIFFERENCE EQUATIONS FOR SHALLOW WATER FLOWS IN ORTHOGOPNAL COORDINATES

The partial differential equations for 2D shallow water flows are formulated in the orthogonal boundary-fitted coordinate systems, and solved on a space-staggered grid with ADI scheme. The finite difference approximations to the 2D shallow water equations are obtained to have all terms except water level in continuity equation folly centered in both space and time by iteration. The representation of continuity equation shows 1-and 2-order accuracy in time and space respectively. while the representations of momentum equations display 2-order accuracy in both time and space. Stability analysis reveals these representations should still conform to the CFL condition. The solution technique for the governing equations is verified by comparing the model output with field data. and the agreement is encouraging.