259 RWTH Publication No: 47205        2006        IGPM259.pdf
TITLE Well-Balanced Finite Volume Evolution Galerkin Methods for the Shallow Water Equations
AUTHORS Maria Lukáčová-Medviďová, Sebastian Noelle, Marcus Kraft
ABSTRACT We present a new well-balanced finite volume method within the framework of the finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for the shallow water equations with source terms modelling the bottom topography and Coriolis forces. Results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are taken into account explicitly. We derive a well-balanced approximation of the integral equations and prove that the FVEG scheme is well-balanced for the stationary steady states as well as for the steady jets in the rotational frame. Several numerical experiments for stationary and quasi-stationary states as well as for steady jets confirm the reliability of the well-balanced FVEG scheme.
KEYWORDS well-balanced schemes, steady states, systems of hyperbolic balance laws, shallow water equations, geostrophic balance, evolution Galerkin schemes
DOI 10.1016/j.jcp.2006.06.015
PUBLICATION Journal of computational physics
221(1), 122-147 (2007)