an:01421622
Zbl 0961.76047
Bermúdez, Alfredo; Dervieux, Alain; Desideri, Jean-Antoine; Vázquez, M. Elena
Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes
EN
Comput. Methods Appl. Mech. Eng. 155, No. 1-2, 49-72 (1998).
0045-7825
1998
j
76M12 76B15 86A05 86-08
shallow water equations; two-dimensional Saint-Venant equations; upwind schemes; hyperbolic equations; unstructured meshes; finite volumes; source term; conservation property; tidal flows; Pontevedra ria
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.