Discrete asymptotic equations for long wave propagation

S Bellec (1) , Mathieu Colin (1) , Mario Ricchiuto (1)

1 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts

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 then performing 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.

Mots clés: Wave propagation; asymptotic equations; discrete asymptotics; Boussinesq models; finite elements

Domaines: Modélisation et simulation; Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Océan, Atmosphère

S Bellec, Mathieu Colin, Mario Ricchiuto. Discrete asymptotic equations for long wave propagation. [Research Report] RR-8806, Inria Bordeaux Sud-Ouest. 2015, pp.29. ⟨hal-01224157⟩