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Journal Articles SIAM Journal on Numerical Analysis Year : 2016

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.

Dates and versions

hal-01378612 , version 1 (10-10-2016)

Identifiers

Cite

Stevan Bellec, Mathieu Colin, Mario Ricchiuto. Discrete asymptotic equations for long wave propagation. SIAM Journal on Numerical Analysis, 2016, 54 (6), pp.3280-3299. ⟨10.1137/15M104325X⟩. ⟨hal-01378612⟩
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