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A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation. (English) Zbl 1290.35194
The main purpose of this paper is to derive a new multilayer Saint-Venant model where the unknowns are a total height of water and an average velocity per layer. This model deals with the total height of water, which leads to a global continuity equations and allows mass exchanges between layers. Then the main properties of the multilayer model are presented, and a kinetic interpretation of this model leads to a effective numerical scheme with positivity and energy properties. Some numerical analysis are given.
Reviewer: Cheng He (Beijing)

MSC:
35Q35 PDEs in connection with fluid mechanics
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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