Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant
Journal of Scientific Computing
High order resolution of the Maxwell-Fokker-Planck-Landau model intended for ICF applications
Journal of Computational Physics
Journal of Computational Physics
A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
Journal of Computational Physics
Numerical Simulation of Strongly Nonlinear and Dispersive Waves Using a Green---Naghdi Model
Journal of Scientific Computing
Efficient well-balanced hydrostatic upwind schemes for shallow-water equations
Journal of Computational Physics
A Local Entropy Minimum Principle for Deriving Entropy Preserving Schemes
SIAM Journal on Numerical Analysis
On the well-balanced numerical discretization of shallow water equations on unstructured meshes
Journal of Computational Physics
A kinetic flux-vector splitting method for single-phase and two-phase shallow flows
Computers & Mathematics with Applications
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The VFRoe scheme has been recently introduced by Buffard, Gallouët, and Hérard [Comput. Fluids, 29 (2000), pp. 813-847] to approximate the solutions of the shallow water equations. One of the main interests of this method is to be easily implemented. As a consequence, such a scheme appears as an interesting alternative to other more sophisticated schemes. The VFRoe methods perform approximate solutions in good agreement with the expected ones. However, the robustness of this numerical procedure has not been proposed. Following the ideas introduced by Jin and Xin [Comm. Pure Appl. Math., 45 (1995), pp. 235-276], a relevant relaxation method is derived. The interest of this relaxation scheme is twofold. In the first hand, the relaxation scheme is shown to coincide with the considered VFRoe scheme. In the second hand, the robustness of the relaxation scheme is established, and thus the nonnegativity of the water height obtained involving the VFRoe approach is ensured. Following the same idea, a family of relaxation schemes is exhibited. Next, robust high order slope limiter methods, known as MUSCL reconstructions, are proposed. The final scheme is obtained when considering the hydrostatic reconstruction to approximate the topography source terms. Numerical experiments are performed to attest the interest of the procedure.