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Finite-volume solvers for a multilayer Saint-Venant system. (English) Zbl 1152.35305
Summary: We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to 3D hydrostatic Navier-Stokes equations.

MSC:
35A35 Theoretical approximation in context of PDEs
35L10 Second-order hyperbolic equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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