. Some approximate Godunov schemes to compute shallow-water equations with topography. Computers and Fluids, Elsevier, 2003, 32 (4)
AbstractWe study here the computation of shallow-water equations with topography by Finite Volume methods, in a one-dimensional framework (though all methods introduced may be naturally extended in two dimensions). All methods performed are based on a dicretisation of the topography by a piecewise function constant on each cell of the mesh, from an original idea of A.Y. Le Roux et al.. Whereas the Well-Balanced scheme of A.Y. Le Roux is based on the exact resolution of each Riemann problem, we consider here approximate Riemann solvers, namely the VFRoencv schemes. Several single step methods are derived from this formalism, and numerical results are compared to a fractional step method. Some tests cases are presented : convergence to steady states in subcritical and supercritical con gurations, occurence of dry area by a drain over a bump and occurence of vacuum by a double rarefaction wave over a step. Numerical schemes, combined with an appropriate high order extension, provide accurate and convergent approximations.
Closure laws for interfacial pressure and interfacial velocity are proposed within the frame of two-pressure two-phase flow models. These enable to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. Lois de fermeture pour un modèleà deux pressions d'écoulement diphasique Résumé. On propose des lois de fermeture de vitesse et de pression d'interface pour un modèle d'écoulement diphasiqueà deux pressions. Celles-ci assurent champ par champ de respecter la positivité des fractions volumiques, des variables densité eténergie interne si on examine le problème de Riemann.
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