270 | IGPM270.pdf January 2007 |
TITLE | High Order Well-Balanced Finite Volume WENO Schemes for Shallow Water Equation with Moving Water |
AUTHORS | Sebastian Noelle, Yulong Xing, Chi-Wang Shu |
ABSTRACT | A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Recently a number of so-called well-balanced schemes were developed which satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. In most cases, applications treated equilibria at rest, where the flow velocity vanishes. Here we present a new very high order accurate, exactly well- balanced finite volume scheme for moving flow equilibria. Numerical experiments show excellent resolution of unperturbed as well as slightly perturbed equilibria. |
KEYWORDS | shallow water equation, moving water equilibria, high order upwind finite volume scheme, well-balanced scheme |
DOI | 10.1016/j.jcp.2007.03.031 |
PUBLICATION | Journal of computational physics 226(1), 29-58 (2007) |