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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.

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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