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Well-balanced second-order finite element approximation of the shallow water equations with friction. (English) Zbl 1405.65120

Summary: This paper investigates the approximation of the shallow water equations with topography and friction, using continuous finite elements. A new, second-order, parameter-free, well-balanced and positivity preserving explicit approximation technique is introduced. The novelties of the method are the explicit treatment of the friction term, the robust approximation of dry states, a commutator-based, high-order, entropy viscosity, and a local limiting procedure. The computational method is illustrated on various benchmark tests.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L50 Initial-boundary value problems for first-order hyperbolic systems
35L65 Hyperbolic conservation laws
76M10 Finite element methods applied to problems in fluid mechanics
35Q35 PDEs in connection with fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction

Software:

SHASTA; SWASHES
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Full Text: DOI

References:

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