A Godunov-type finite volume method for the system of shallow water equations. (English) Zbl 0916.76051
Summary: We develop a finite volume based numerical algorithm 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 two dimensions 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. Additionally, the basic Godunov method is extended to second-order accuracy through a slope-limiter-type algorithm.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
Keywords:
Riemann problem; Roe’s technique; complex coastal flow problems; second-order accuracy; slope-limiter-type algorithmReferences:
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