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Discrete asymptotic equations for long wave propagation

Abstract : In this paper, we present a new systematic method to obtain some discrete numerical models for incompressible free-surface flows.The method consists in first discretizing the Euler equations with respect to one variable, keeping the other ones unchanged and thenperforming an asymptotic analysis on the resulting system. For the sake of simplicity, we choose to illustrate this method in the context of the Peregrine asymptotic regime, that is we propose an alternative numerical scheme for the so-called Peregrine equations.We then study the linear dispersion characteristics of our new scheme and present several numerical experiments to measure the relevance of the method.
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https://hal.inria.fr/hal-01378612
Contributor : Mathieu Colin <>
Submitted on : Monday, October 10, 2016 - 2:59:25 PM
Last modification on : Thursday, January 11, 2018 - 6:27:21 AM

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  • HAL Id : hal-01378612, version 1

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Stevan Bellec, Mathieu Colin, Mario Ricchiuto. Discrete asymptotic equations for long wave propagation. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2016. ⟨hal-01378612⟩

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