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Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation. (English) Zbl 0997.76023
Summary: We derive the Saint-Venant system for shallow water including small friction, viscosity and Coriolis-Boussinesq factor departing from the Navier-Stokes system with a free moving boundary. This derivation relies on the hydrostatic approximation where we follow the role of viscosity and friction on the bottom. Numerical comparisons between the limiting Saint-Venant system and direct Navier-Stokes simulation allow to validate this derivation.

MSC:
76D33 Waves for incompressible viscous fluids
76M12 Finite volume methods applied to problems in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
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