Non-dispersive conservative regularisation of nonlinear shallow water and isothermal Euler equations

Abstract

A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and possess 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.

Keywords

Bibliographic record

BibTeX Citation

@article{Clamond2018nondispersiveconservative,
  author = {Clamond, D. and Dutykh, D.},
  title = {Non-dispersive conservative regularisation of nonlinear shallow water and isothermal Euler equations},
  journal = {Commun. Nonlinear Sci. Numer. Simulat.},
  year = {2018},
  volume = {55},
  pages = {237--247},
  doi = {10.1016/j.cnsns.2017.07.011},
  abstract = {A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and possess 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.},
  keywords = {Shallow water flows, Conservative, Dispersionless, Regularisation}
}