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Application of the WAF Method to Shallow Water Equations with Pollutant and Non-Constant Bottom

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • E. D. Fernández-Nieto

    (Universidad de Sevilla, Dpto. de Matemática Aplicada I, E.T.S. Arquitectura)

  • G. Narbona-Reina

    (Universidad de Sevilla, Dpto. de Matemática Aplicada I, E.T.S. Arquitectura)

Abstract

In this work we perform the extension of the WAF method [3] to discretize non-homogeneous Shallow Water Equations with pollutant. We propose a well-balanced extension: the numerical scheme preserves all stationary solutions up to second order, and exactly preserves water at rest. The difficulty lies in the treatment of the pollutant component that includes an extra term related with the approximation of the intermediate wave. Finally, we perform several numerical tests, by comparing it with the HLLC solver, analytical solutions and reference solutions.

Suggested Citation

  • E. D. Fernández-Nieto & G. Narbona-Reina, 2008. "Application of the WAF Method to Shallow Water Equations with Pollutant and Non-Constant Bottom," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 273-280, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_32
    DOI: 10.1007/978-3-540-69777-0_32
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