High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms

By Yulong Xing, Chi-Wang Shu. Journal of Computational Physics, 2006

347 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A Survey of High Order Schemes for the Shallow Water Equations (2014, methodology): “In this section, we recall the positivity-preserving high order well-balanced finite element DG schemes developed by us in [55, 59, 60, 64, 65].”
A well‐balanced Runge–Kutta discontinuous Galerkin method for the shallow‐water equations with flooding and drying (2008, positive): “Concerning the evaluation of the source term, both schemes introduce additional terms (involving the L(2)-projection of b onto PpD); the present well-balanced DG scheme introduces only a high-order boundary perturbation, whereas the scheme proposed in [30] first splits the source term into two contr”
High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems (2009, methodology): “A procedure to systematically modify the WENO procedure so that it is still stable and nonoscillatory in the presence of negative weights was developed in [146] and has been used in many later works, such as in [131], where this technique is used to construct high order central WENO schemes, in [127”
High-order balanced CWENO scheme for movable bed shallow water equations (2007, methodology): “In the paper of Xing and Shu [38] a high-order finite volume upwind WENO scheme and a Runge-Kutta discontinuous Galerkin finite element method are extended to a class of hyperbolic system of balance laws with separable source terms.”