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Numerical Scheme for a Viscous Shallow Water System Including New Friction Laws of Second Order: Validation and Application

  • Olivier Delestre
  • Ulrich RazafisonEmail author
Chapter
Part of the Springer Water book series (SPWA)

Abstract

In this work, we are interested in the derivation of a new shallow water model with a diffusion source term. Analytical solutions for steady flow regimes are first presented to validate a numerical method designed to solve this new model. Then this model is applied on real data and seems to give better results than the classical shallow water system.

Keywords

Shallow water system Model derivation Finite volume scheme Well-balanced method Hydrostatic reconstruction Friction law Manning friction law Darcy-Weisbach friction law 

Notes

Acknowledgements

The authors whish to thanks the ANR-11-JS01-006-01 project CoToCoLa (Contemporary Topics on Conservation Laws), Carine Lucas for her advices and Frédéric Darboux for the data used in Sect. 4.2.

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Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Laboratory J.A. Dieudonné CNRS UMR 7351 & Polytech Nice – SophiaUNSAArequipaPeru
  2. 2.Laboratoire de Mathématiques, CNRS UMR 6623Université de Franche-ComtéBesançon CedexFrance

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