Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
Journal of Scientific Computing
SIAM Journal on Scientific Computing
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
Journal of Computational Physics
On maximum-principle-satisfying high order schemes for scalar conservation laws
Journal of Computational Physics
A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows
SIAM Journal on Numerical Analysis
On the Advantage of Well-Balanced Schemes for Moving-Water Equilibria of the Shallow Water Equations
Journal of Scientific Computing
Hi-index | 31.45 |
Hyperbolic conservation laws with source terms often admit steady state solutions where the fluxes and source terms balance each other. To capture this balance and near-equilibrium solutions, well-balanced methods have been introduced and performed well in many numerical tests. Shallow water equations have been extensively investigated as a prototype example. In this paper, we develop well-balanced discontinuous Galerkin methods for the shallow water system, which preserve not only the still water at rest steady state, but also the more general moving water equilibrium. The key idea is the recovery of well-balanced states, a special source term approximation, and the approximation of the numerical fluxes based on a generalized hydrostatic reconstruction. We also study the extension of the positivity-preserving limiter presented in [40] in this framework. Numerical examples are provided at the end to verify the well-balanced property and good resolution for smooth and discontinuous solutions.