Toward the ultimate conservative scheme: following the quest
Journal of Computational Physics
Journal of Computational Physics
High Order Fluctuation Schemes on Triangular Meshes
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Residual distribution for general time-dependent conservation laws
Journal of Computational Physics
Journal of Computational Physics
Stabilized residual distribution for shallow water simulations
Journal of Computational Physics
High-order well-balanced schemes and applications to non-equilibrium flow
Journal of Computational Physics
A Hybrid Second Order Scheme for Shallow Water Flows
Journal of Scientific Computing
Hybrid Second Order Schemes for Scalar Balance Laws
Journal of Scientific Computing
A numerical treatment of wet/dry zones in well-balanced hybrid schemes for shallow water flow
Applied Numerical Mathematics
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In this paper we consider the discretization of the Shallow Water equations by means of Residual Distribution (RD) schemes. We review the conditions allowing the exact preservation of some exact steady solutions. These conditions are shown to be related both to the type of spatial approximation and to the quadrature used to evaluate the cell residual. Numerical examples are shown to validate the theory.