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

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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https://hal.archives-ouvertes.fr/hal-01232370
Contributor : Denys Dutykh <>
Submitted on : Wednesday, October 12, 2016 - 4:56:37 PM
Last modification on : Thursday, March 5, 2020 - 12:20:08 PM
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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, Elsevier, 2017, 45, pp.245-257. ⟨10.1016/j.cnsns.2016.10.009⟩. ⟨hal-01232370v3⟩

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