Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Flux difference splitting and the balancing of source terms and flux gradients
Journal of Computational Physics
The surface gradient method for the treatment of source terms in the shallow-water equations
Journal of Computational Physics
A well-balanced gas-kinetic scheme for the shallow-water equations with source terms
Journal of Computational Physics
Journal of Computational Physics
WENO schemes for balance laws with spatially varying flux
Journal of Computational Physics
Journal of Computational Physics
Approximation of Hyperbolic Models for Chemosensitive Movement
SIAM Journal on Scientific Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Journal of Scientific Computing
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Journal of Computational Physics
Fourth-order balanced source term treatment in central WENO schemes for shallow water equations
Journal of Computational Physics
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Shallow water model on cubed-sphere by multi-moment finite volume method
Journal of Computational Physics
Stabilized residual distribution for shallow water simulations
Journal of Computational Physics
High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems
Journal of Scientific Computing
Journal of Computational Physics
High-order well-balanced schemes and applications to non-equilibrium flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Mathematics and Computers in Simulation
Journal of Scientific Computing
A Hybrid Second Order Scheme for Shallow Water Flows
Journal of Scientific Computing
A numerical treatment of wet/dry zones in well-balanced hybrid schemes for shallow water flow
Applied Numerical Mathematics
Efficient well-balanced hydrostatic upwind schemes for shallow-water equations
Journal of Computational Physics
Advances in Engineering Software
Hybrid Well-balanced WENO Schemes with Different Indicators for Shallow Water Equations
Journal of Scientific Computing
On the well-balanced numerical discretization of shallow water equations on unstructured meshes
Journal of Computational Physics
High Order Well-Balanced WENO Scheme for the Gas Dynamics Equations Under Gravitational Fields
Journal of Scientific Computing
Energy balance numerical schemes for shallow water equations with discontinuous topography
Journal of Computational Physics
A Well-Balanced Reconstruction of Wet/Dry Fronts for the Shallow Water Equations
Journal of Scientific Computing
High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model
Journal of Computational Physics
Journal of Computational Physics
Well-Balanced Adaptive Mesh Refinement for shallow water flows
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.54 |
Shallow water equations with nonflat bottom have steady state solutions in which the flux gradients are nonzero but exactly balanced by the source term. It is a challenge to design genuinely high order accurate numerical schemes which preserve exactly these steady state solutions. In this paper we design high order finite difference WENO schemes to this system with such exact conservation property (C-property) and at the same time maintaining genuine high order accuracy. Extensive one and two dimensional simulations are performed to verify high order accuracy, the exact C-property, and good resolution for smooth and discontinuous solutions.