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Large Time Step Finite Volume Evolution Galerkin Methods

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Abstract

We present two new large time step methods within the framework of the well-balanced finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for low Froude number shallow water flows with source terms modeling the bottom topography and Coriolis forces, but 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 present two variants of large time step FVEG method: a semi-implicit time approximation and an explicit time approximation using several evolution steps along bicharacteristic cones.

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Authors and Affiliations

  1. Institute of Mathematics, University of Mainz, Staudingerweg 9, 55099, Mainz, Germany

    A. Hundertmark-Zaušková, M. Lukáčová-Medvid’ová & F. Prill

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  1. A. Hundertmark-Zaušková
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  2. M. Lukáčová-Medvid’ová
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  3. F. Prill
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Corresponding author

Correspondence to M. Lukáčová-Medvid’ová.

Additional information

This research has been supported by the German Research Foundation DFG under the grant LU 1470/2-1.

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Hundertmark-Zaušková, A., Lukáčová-Medvid’ová, M. & Prill, F. Large Time Step Finite Volume Evolution Galerkin Methods. J Sci Comput 48, 227–240 (2011). https://doi.org/10.1007/s10915-010-9443-5

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  • DOI: https://doi.org/10.1007/s10915-010-9443-5

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