Modified shallow water equations for significantly varying seabeds

Denys Dutykh, Didier Clamond

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


In the present study, we propose a modified version of the Nonlinear Shallow Water Equations (Saint-Venant or NSWE) for irrotational surface waves in the case when the bottom undergoes some significant variations in space and time. The model is derived from a variational principle by choosing an appropriate shallow water ansatz and imposing some constraints. Our derivation procedure does not explicitly involve any small parameter and is straightforward. The novel system is a non-dispersive non-hydrostatic extension of the classical Saint-Venant equations. A key feature of the new model is that, like the classical NSWE, it is hyperbolic and thus similar numerical methods can be used. We also propose a finite volume discretisation of the obtained hyperbolic system. Several test-cases are presented to highlight the added value of the new model. Some implications to tsunami wave modeling are also discussed.

Original languageBritish English
Pages (from-to)9767-9787
Number of pages21
JournalApplied Mathematical Modelling
Issue number23-24
StatePublished - 1 Dec 2016


  • Finite volumes
  • Saint-Venant equations
  • Shallow water
  • UNO scheme


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