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    Item type:Publication, Access status: without files ,
    Well-balanced bicharacteristic-based scheme for multilayer shallow water flows including wet/dry fronts
    (Elsevier, 2012-11-15)
    Dudzinski, Michael
    ;
    Lukáčová-Medviďová, Mária
    The aim of this paper is to present a new well-balanced finite volume scheme for two-dimensional multilayer shallow water flows including wet/dry fronts. The ideas, presented here for the two-layer model, can be generalized to a multilayer case in a straightforward way. The method developed here is constructed in the framework of the Finite Volume Evolution Galerkin (FVEG) schemes. The FVEG methods couple a finite volume formulation with evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems. However, in the case of multilayer shallow water flows the required eigenstructure of the underlying equations is not readily available. Thus we approximate the evolution operators numerically. This approximation procedure can be used for arbitrary hyperbolic systems. We derive a well-balanced approximation of the evolution operators and prove that the FVEG scheme is well-balanced for the multilayer lake at rest states even in the presence of wet/dry fronts. Several numerical experiments confirm the reliability and efficiency of the new well-balanced FVEG scheme.
    Publicationtype: Journal Article
      105
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    Item type:Publication, Access status: without files ,
    Well-balanced path-consistent finite volume eg schemes for the two-layer shallow water equations
    (Springer, 2011)
    Dudzinski, Michael
    ;
    Medviďová-Lukáčová, Mária
    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.
    Publicationtype: Conference Paper
      6