305 IGPM305.pdf        February 2010
TITLE Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds
AUTHORS Andreas Bollermann, Sebastian Noelle, Maria Lukáčová-Medviďová
ABSTRACT We present a new Finite Volume Evolution Galerkin (FVEG) scheme for the solution of the shallow water equations (SWE) with the bottom topography as a source term. Our new scheme will be based on the FVEG methods presented in (Lukáčová, Noelle and Kraft, J. Comp. Phys. 221, 2007), but adds the possibility to handle dry boundaries. The most important aspect is to preserve the positivity of the water height. We present a general approach to ensure this for arbitrary finite volume schemes. The scheme is also well-balanced and a new entropy fix improves the reproduction of sonic rarefaction waves.
KEYWORDS Well-balanced schemes, dry boundaries, shallow water equations, evolution Galerkin schemes, source terms
DOI Well–balanced schemes, dry boundaries, shallow water equatio
PUBLICATION Communications in computational physics
CiCP 10(2), 371-404 (2011)