Non-dispersive conservative regularisation of nonlinear shallow water (and isentropic Euler equations)

Didier Clamond, Denys Dutykh

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and posses a variational structure; thus, the mass, the momentum and the energy are conserved. Hence, for instance, regularised hydraulic jumps are smooth and non-oscillatory. Another particularly interesting feature of this regularisation is that smoothed ‘shocks’ propagates at exactly the same speed as the original discontinuous ones. The performance of the new model is illustrated numerically on some dam-break test cases, which are classical in the hyperbolic realm.

Original languageBritish English
Pages (from-to)237-247
Number of pages11
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume55
DOIs
StatePublished - Feb 2018

Keywords

  • Conservative
  • Dispersionless
  • Regularisation
  • Shallow water flows

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