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# Well-balanced path-consistent finite volume eg schemes for the two-layer shallow water equations

Publikationstyp

Conference Paper

Publikationsdatum

2011

Sprache

English

First published in

Number in series

115

Volume

115

Start Page

121

End Page

135

Citation

Computational Science and High Performance Computing IV : The 4th Russian-German Advanced Research Workshop, Freiburg, Germany, October 12 to 16, 2009 . - Berlin, 2011. - (Notes on Numerical Fluid Mechanics and Multidisciplinary Design ; 115). - Seite 121-135

Publisher DOI

Scopus ID

Publisher

Springer Berlin Heidelberg

ISBN

978-3-642-17770-5

978-3-642-17769-9

We present a new path-consistent well-balanced finite volume method within the framework of the evolution Galerkin (FVEG) schemes. The methodology will be illustrated for two layer shallow water equations with source terms modelling the bottom topography and Coriolis forces. 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 will derive a suitable path in the phase space that is based on the evolution operator and derive the corresponding path-consistent FVEG scheme. The path-consistent FVEG scheme is well-balanced for the stationary steady states as well as for the steady jets in the rotational frame. © 2011 Springer-Verlag Berlin Heidelberg.