Well-Balanced Path-Consistent Finite Volume EG Schemes for the Two-Layer Shallow Water Equations
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.
KeywordsCoriolis Force Bottom Topography Shallow Water Equation Rotational Frame Shallow Water System
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- 5.Frings, J.: Well-Balanced Finite Volumes of Higher Order of Accuracy for Two-Layer Shallow Water Flows. Master Thesis, RWTH Aachen (2007)Google Scholar