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.
Domains
Fluid mechanics [physics.class-ph] Atmospheric and Oceanic Physics [physics.ao-ph] Fluid Dynamics [physics.flu-dyn] Analysis of PDEs [math.AP] Mathematical Physics [math-ph] Computational Physics [physics.comp-ph] Geophysics [physics.geo-ph] Exactly Solvable and Integrable Systems [nlin.SI] Pattern Formation and Solitons [nlin.PS]Origin | Files produced by the author(s) |
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