Conservative multidimensional upwinding for the steady two-dimensional shallow water equations
Journal of Computational Physics
Toward the ultimate conservative scheme: following the quest
Journal of Computational Physics
Residual Distribution Schemes for Conservation Laws via Adaptive Quadrature
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
High Order Fluctuation Schemes on Triangular Meshes
Journal of Scientific Computing
Journal of Computational Physics
A second-order-accurate monotone implicit fluctuation splitting scheme for unsteady problems
Journal of Computational Physics
Journal of Computational Physics
Residual distribution for general time-dependent conservation laws
Journal of Computational Physics
Essentially non-oscillatory Residual Distribution schemes for hyperbolic problems
Journal of Computational Physics
Third-order-accurate fluctuation splitting schemes for unsteady hyperbolic problems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
On uniformly high-order accurate residual distribution schemes for advection-diffusion
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
High-order well-balanced schemes and applications to non-equilibrium flow
Journal of Computational Physics
Explicit Runge-Kutta residual distribution schemes for time dependent problems: Second order case
Journal of Computational Physics
Journal of Scientific Computing
Large Time Step Finite Volume Evolution Galerkin Methods
Journal of Scientific Computing
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
On the well-balanced numerical discretization of shallow water equations on unstructured meshes
Journal of Computational Physics
A Well-Balanced Reconstruction of Wet/Dry Fronts for the Shallow Water Equations
Journal of Scientific Computing
Hi-index | 31.46 |
We propose a stabilized Residual Distribution (RD) scheme for the simulation of shallow water flows. The final discretization is obtained combining the stabilized RD approach proposed in (Abgrall, J. Comp. Phys. 214, 2006) and (Ricchiuto and Abgrall, ICCFD4, Springer-Verlag 2006), with the conservative formulation already used in (Ricchiuto et al., J. Comp. Phys. 222, 2007) to simulate shallow water flows. The scheme proposed is a nonlinear variant of a Lax-Friedrichs type discretization. It is well balanced, it actually yields second-order of accuracy in smooth areas, and it preserves the positivity of the height of the water in presence of dry areas. This is made possible by the residual character of the discretization, by properly adapting the stabilization operators proposed in (Abgrall, J. Comp. Phys. 214, 2006) and (Ricchiuto and Abgrall, ICCFD4, Springer-Verlag, 2006), and thanks to the positivity preserving character of the underlying Lax-Friedrichs scheme. We demonstrate the properties of the discretization proposed on a wide variety of tests.