Numerical Solutiion of the Two-Dimensional Shallow Water Equations By the Finite Volume Method and Its Application

Numerical solutions of the 2-dimensional shallow water equations by the finite volume method (FVM) are presented. The governing equations are expressed in a hyperbolic conservation law to conserve both momentum and mass. Inviscid normal fluxes at cell faces are estimated using a Riemann solver. The numerical model uses the combination of triangular and quadrilateral grids to fit complex boundaries better, and the model includes wetting and drying processes. The numerical model results are verified with known analytical solutions such as the dam-breaking problem. The model is found to give accurate results in comparison with published analytical and alternative numerical solutions. After verifying the numerical results, the model is successfully applied to wind circulation in a reservoir.