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A comparison between the meshless and the finite volume methods for shallow water flows

  • Yasser Alhuri
  • Fayssal Benkhaldoun
  • Imad Elmahi
  • Driss Ouazar
  • Mohammed Seaïd
  • Ahmed Taik
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 4)

Abstract

A numerical comparison is presented between a meshless method and a finite volume method for solving the shallow water equations. The meshless method uses the multiquadric radial basis functions whereas a modified Roe reconstruction is used in the finite volume method. The obtained results using both methods are compared to experimental measurements.

Keywords

Meshless method shallow water equations finite volume method radial basis functions numerical simulation 

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Notes

Acknowledgements

The authors would like to thank Prof. Jaime Fe Marqués for providing the experimental data to us.

References

  1. 1.
    F. Benkhaldoun, I. Elmahi, M. Seaïd, “A new finite volume method for flux-gradient and source-term balancing in shallow water equations”, Computer Methods in Applied Mechanics and Engineering. 199 pp:49-52 (2010).CrossRefGoogle Scholar
  2. 2.
    F. Benkhaldoun, I. Elmahi, M. Seaïd, “Well-balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes”, J. Comp. Physics. 226 pp:180-203 (2007).zbMATHCrossRefGoogle Scholar
  3. 3.
    T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, P. Krysl, “Meshless methods: an overview and recent developments”, Computer methods in applied mechanics and engineering”, special issue on Meshless Methods, 139, pp:3-47, (1996).Google Scholar
  4. 4.
    M. Buhamman, Radial basis function: theory and implementations, Cambridge university press, (2003).Google Scholar
  5. 5.
    R. L. Hardy, “Multiquadric equations of topography and other irregular surfaces”. J. Geophys. Res, 176, pp:1905-1915, (1971).CrossRefGoogle Scholar
  6. 6.
    J. Fe, F. Navarrina, J. Puertas, P. Vellando and D. Ruiz, “Experimental validation of two depth-averaged turbulence models”, Int. J. Numer. Meth. Fluids, 60, pp:177-202, (2009).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Y. C. Hon, K. F. Cheung, X. Z. Mao and E. J. Kansa, “A Multiquadric solution for the shallow water equations”, ASCE J. of hydrodlic engineering”, vol.125, No.5, pp:524-533, (1999).Google Scholar
  8. 8.
    P. Roe, “Approximate riemann solvers, parameter vectors and difference schemes”, J. Comp. Physics. 43, pp:357-372, (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    S. M. Wong, Y.C. Hon, M.A. Golberg, “Compactly supported radial basis functions shallow water equations”, J. Appl. Sci. Comput, 127, 79-101, (2002).MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yasser Alhuri
    • 1
  • Fayssal Benkhaldoun
    • 2
  • Imad Elmahi
    • 3
  • Driss Ouazar
    • 4
  • Mohammed Seaïd
    • 5
  • Ahmed Taik
    • 1
  1. 1.Dept. Mathematics, UFR-MASI FSTHassan II University MohammediaMohammediaMorocco
  2. 2.LAGAUniversité Paris 13VilletaneuseFrance
  3. 3.ENSAO Complex UniversitaireOujdaMorocco
  4. 4.Dept. Genie Civil, LASH EMIMohammed V University RabatRabatMorocco
  5. 5.School of Engineering and Computing SciencesUniversity of DurhamDurhamUK

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