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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.

MSC:
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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