270 RWTH Publication No: 47232        2007        IGPM270.pdf
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)