Few numerical aspects of the Neumann-Kelvin's model with capillary in hydrodynamics

Philippe Destuynder (1) , Caroline Fabre (2) , Olivier Wilk (1)

1 M2N - Modélisation mathématique et numérique
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

A discussion and an improvement on the Neumann-Kelvin's model are suggested in this paper. This model is used in the simulation of progres- sive wave phenomenon. But as mentioned by several authors [CHEN 01], [YAN 00], [RIC 96], [LIH 78], this model is ill posed unless a capillary en- ergy is introduced. The mathematical explanation is that a compactness inversion occurs if the capillary forces are omitted. Theoretical argu- ments and numerical simulations are used in the following which aim at giving an explanation of what happens from a mechanical point of view.

Mots clés: spectral theory; non-linear models; water waves; unstabilities; wave equations

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Destuynder, Caroline Fabre, Olivier Wilk. Few numerical aspects of the Neumann-Kelvin's model with capillary in hydrodynamics. 2009. ⟨hal-00429739⟩