Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
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
Weighted essentially non-oscillatory schemes on triangular meshes
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
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
A well-balanced gas-kinetic scheme for the shallow-water equations with source terms
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Equilibrium schemes for scalar conservation laws with stiff sources
Mathematics of Computation
WENO schemes for balance laws with spatially varying flux
Journal of Computational Physics
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
Journal of Computational Physics
Approximation of Hyperbolic Models for Chemosensitive Movement
SIAM Journal on Scientific Computing
Journal of Scientific Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A first-order system approach for diffusion equation. I: Second-order residual-distribution schemes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant
Journal of Scientific Computing
Stabilized residual distribution for shallow water simulations
Journal of Computational Physics
Computers & Mathematics with Applications
A simple finite volume method for the shallow water equations
Journal of Computational and Applied Mathematics
A multi-moment finite volume formulation for shallow water equations on unstructured mesh
Journal of Computational Physics
Journal of Scientific Computing
On the Advantage of Well-Balanced Schemes for Moving-Water Equilibria of the Shallow Water Equations
Journal of Scientific Computing
Locally Limited and Fully Conserved RKDG2 Shallow Water Solutions with Wetting and Drying
Journal of Scientific Computing
Binary weighted essentially non-oscillatory (BWENO) approximation
Journal of Computational and Applied Mathematics
Hybrid Well-balanced WENO Schemes with Different Indicators for 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
Hi-index | 31.50 |
Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) 206-227; J. Sci. Comput., accepted], we designed a well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which at the same time maintains genuine high order accuracy for general solutions, to a class of hyperbolic systems with separable source terms including the shallow water equations, the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. In this paper, we generalize high order finite volume WENO schemes and Runge-Kutta discontinuous Galerkin (RKDG) finite element methods to the same class of hyperbolic systems to maintain a well-balanced property. Finite volume and discontinuous Galerkin finite element schemes are more flexible than finite difference schemes to treat complicated geometry and adaptivity. However, because of a different computational framework, the maintenance of the well-balanced property requires different technical approaches. After the description of our well-balanced high order finite volume WENO and RKDG schemes, we perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions.