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A Numerical Scheme for a Viscous Shallow Water Model with Friction

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Abstract

We consider a particular viscous shallow water model with topography and friction laws, formally derived by asymptotic expansion from the three-dimensional free surface Navier-Stokes equations. Emphasize is put on the numerical study: the viscous system is regarded as an hyperbolic system with source terms and discretized using a second order finite volume method. New steady states solutions for open channel flows are introduced for the whole model with viscous and friction terms. The proposed numerical scheme is validated against these new benchmarks.

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Authors and Affiliations

  1. Université d’Orléans, MAPMO, Orléans, France

    Olivier Delestre

  2. Université Montpellier 2, I3M, Montpellier, France

    Fabien Marche

Authors
  1. Olivier Delestre
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  2. Fabien Marche
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Correspondence to Olivier Delestre.

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Delestre, O., Marche, F. A Numerical Scheme for a Viscous Shallow Water Model with Friction. J Sci Comput 48, 41–51 (2011). https://doi.org/10.1007/s10915-010-9393-y

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  • DOI: https://doi.org/10.1007/s10915-010-9393-y

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