Skip to Main content Skip to Navigation
Journal articles

Regularised shallow water equations with uneven bottom

Abstract : The regularisation of nonlinear hyperbolic conservation laws has been a problem of great importance for achieving uniqueness of weak solutions and also for accurate numerical simulations. In a recent work, the first two authors proposed a so-called Hamiltonian regularisation for nonlinear shallow water and isentropic Euler equations. The characteristic property of this method is that the regularisation of solutions is achieved without adding any artificial dissipation or dispersion. The regularised system possesses a Hamiltonian structure and, thus, formally preserves the corresponding energy functional. In the present article we generalise this approach to shallow water waves over general, possibly time-dependent, bottoms. The proposed system is solved numerically with continuous Galerkin method and its solutions are compared with the analogous solutions of the classical shallow water and dispersive Serre-Green-Naghdi equations. The numerical results confirm the absence of dispersive and dissipative effects in presence of bathymetry variations.
Complete list of metadata

Cited literature [30 references]  Display  Hide  Download
Contributor : Denys DUTYKH Connect in order to contact the contributor
Submitted on : Monday, September 16, 2019 - 2:02:34 PM
Last modification on : Sunday, June 26, 2022 - 2:40:45 AM


Files produced by the author(s)


Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike 4.0 International License



Didier Clamond, Denys Dutykh, Dimitrios Mitsotakis. Regularised shallow water equations with uneven bottom. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2019, 52, pp.42LT01. ⟨10.1088/1751-8121/ab3eb2⟩. ⟨hal-02140161v2⟩



Record views


Files downloads