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Journal Articles Communications in Nonlinear Science and Numerical Simulation Year : 2017

Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics

Abstract

For surface gravity waves propagating in shallow water, we propose a variant of the fully nonlinear Serre-Green-Naghdi equations involving a free parameter that can be chosen to improve the dispersion properties. The novelty here consists in the fact that the new model conserves the energy, contrary to other modified Serre's equations found in the literature. Numerical comparisons with the Euler equations show that the new model is substantially more accurate than the classical Serre equations, specially for long time simulations and for large amplitudes.
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Dates and versions

hal-01232370 , version 1 (23-11-2015)
hal-01232370 , version 2 (22-01-2016)
hal-01232370 , version 3 (12-10-2016)

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Didier Clamond, Denys Dutykh, Dimitrios Mitsotakis. Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics: Improved Serre-Green-Naghdi equations. Communications in Nonlinear Science and Numerical Simulation, 2017, 45, pp.245-257. ⟨10.1016/j.cnsns.2016.10.009⟩. ⟨hal-01232370v3⟩
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