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Genuinely multidimensional evolution Galerkin schemes for the shallow water equations

  • M. Lukáčová-Medvid’ová
  • J. Saibertová

Summary

The main objective of this contribution is to present a new genuinely multidimensional finite volume scheme for the shallow water equations. Our approach couples a finite volume formulation with an approximate evolution operator. The latter is constructed using bicharacteristics of the multidimensional hyperbolic system, such that all of the infinitely many directions of wave propagation are taken into account. In order to achieve monotone and genuinely multidimensional FV scheme it is suitable to use Simpson’s rule approximation of the flux integrals along the cell interfaces. The experimental tests confirm good multidimensional properties of the scheme, e.g., preservation of rotational symmetry and monotonicity.

Keywords

Finite Volume Hyperbolic System Shallow Water Equation Hydraulic Jump Cell Interface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Fey, M. (1998): Multidimensional upwinding. II. Decomposition of the Euler equations into advection equations. J. Comput. Phys.143, 181–199MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Lukáčová-Medvid’ová, M., Morton, K.W., Warnecke, G. (2000): Evolution Galerkin methods for hyperbolic systems in two space dimensions. Math. Comp. 69, 1355–1384MathSciNetCrossRefGoogle Scholar
  3. [3]
    Lukáčová-Medvid’ová, M., Morton, K.W., Warnecke, G. (1999): Finite volume evolution Galerkin methods for multidimensional hyperbolic problems. In: Vilsmeier, R. et al. (eds.): Finite volumes for complex applications. II. Hermès, Paris, pp. 289–296Google Scholar
  4. [4]
    Lukáčová-Medvid’ová, M., Morton, K.W, Warnecke, G. (2003): High-order evolution Galerkin schemes for multidimensional hyperbolic systems, in preparationGoogle Scholar
  5. [5]
    Lukáčová-Medvid’ová, M., Saibertová, J., Warnecke,G. (2003): Finite volume evolution Galerkin methods for nonlinear hyperbolic systems. J. Comput. Phys., submittedGoogle Scholar
  6. [6]
    Noelle, S. (2000): The MoT-ICE: a new high-resolution wave-propagation algorithm for multidimensional systems of conservative laws based on Fey’s method of transport. J. Comput. Phys. 164, 283–334MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Ostkamp, S. (1995): Multidimensional characterisitic Galerkin schemes and evolution operators for hyperbolic systems. DLR Forschungsbericht 95-20. DLR, Köln 155–164Google Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • M. Lukáčová-Medvid’ová
    • 1
  • J. Saibertová
    • 2
  1. 1.AB MathematikTechnische Universität Hamburg-HarburgHamburgGermany
  2. 2.Institute of MathematicsUniversity of Technology BrnoBrnoCzech Republic

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