A Godunov-type finite volume method for the system of Shallow Water Equations

A finite volume based numerical algorithm has been developed for the numerical solution of the system of shallow water equations. The algorithm is a Godunov type method and solves the Riemann problem approximately using Roe's technique. The algorithm is developed in 2-D with arbitrary triangulations and conserves all primary variables such as mass and momentum. The procedure is implemented on some simple test cases and some complex coastal flow problems. The algorithm is shown to produce excellent results without spurious oscillations and agrees very well with known analytical results and predictions made by wave equation formulations of the shallow water equations. The basic Godunov method is also extended to second-order accuracy through a slope-limiter type algorithm.