Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes. (English) Zbl 0961.76047

Summary: We extend certain well-known upwind schemes for hyperbolic equations to solve two-dimensional Saint-Venant (or shallow water) equations. We consider unstructured meshes and a new type of finite volumes to obtain a treatment of boundary conditions. The source term involving the gradient of depth is upwinded in a similar way as the flux terms. The resulting schemes are compared in terms of a conservation property. For time discretization, we consider both explicit and implicit schemes. Finally, we present numerical results for tidal flows in the Pontevedra ria, Galicia, Spain.


76M12 Finite volume methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
86A05 Hydrology, hydrography, oceanography
86-08 Computational methods for problems pertaining to geophysics


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