Towards a Two-dimensional Modelling Element in River Flow Simulation Systems

  • M. Schulz
  • G. Steinebach
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 1)

Abstract

For the simulation of water flow in rivers presently a network approach is applied. This approach is based on coupled ld models and should be extended to 2d submodel elements. Special difficulties arise due to the free boundaries caused by the wetting and drying and the source terms accounting for the sloping river bed and friction.

A first order Roe scheme is adapted to these difficulties and is presented for a robust numerical solution method.

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References

  1. 1.
    M. Schulz, G. Steinebach: Twodimensional Modelling of the River Rhine. 8’2000, submitted to Journal of Computational and Applied Mathematics.Google Scholar
  2. 2.
    M.Schulz, G.Steinebach: Towards a Two-dimensional Modelling Element in River Flow Simulation Systems. IWRMM Preprint, Karlsruhe 2000.Google Scholar
  3. 3.
    M.Schulz, G.Steinebach: Modelling and numerical aspects in 2d river flow simulation. 5’2001, submitted to GAMM 2001 ProceedingsGoogle Scholar
  4. 4.
    M. Nujic: Efficient Implementation of Non-Oscillatory Schemes for the Computation of Free-Surface Flows. Journal of Hydraulic Resarch, 33 (1995) No.l.Google Scholar
  5. 5.
    P. Garcia-Navorro, M. Vazquez-Cendon: On the Numerical Treatment of Source Terms in the Shallow Water Equations. To appear in Computer and Fluids.Google Scholar
  6. 6.
    A. Haasenritter: Risk Analysis for Floods by Simulation of Shallow Water Flow. Diploma Thesis, University of Kaiserslautern, Department of Mathematics, 1999.Google Scholar
  7. 7.
    P. Rentrop, G. Steinebach: A Method of Lines Approach for River Alarm Systems. In: M. Br0ns et al.: Progress in Industrial Mathematics at ECMI 96. Teubner, Stuttgart 1997.Google Scholar
  8. 8.
    E.F. Toro: Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, Berlin, Heidelberg 1999.Google Scholar
  9. 9.
    E.F. Toro: The Dry-Bed-Problem in Shallow Water Flows, College of Aeronautics Report No. 9007, 1990.Google Scholar
  10. 10.
    G. Steinebach, A.Q.T. Ngo: A Method of Lines Flux-Difference Splitting Finite Volume Approach for ld and 2d River Flow Problems. To Appear in Godunov Methods: Theory and Applications, E. F. Toro (ed), Kluwer Academic/Plenum Publishers, 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • M. Schulz
    • 1
  • G. Steinebach
    • 2
  1. 1.IWRMMUniversity of KarlsruheGermany
  2. 2.German Federal Institute for HydrologyKoblenzGermany

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