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hal-00429739, version 1

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

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

Abstract: 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.

  • 1:  Conservatoire National des Arts et Métiers (CNAM Paris)
  • Conservatoire National des Arts et Métiers (CNAM)
  • 2:  Laboratoire de Mathématiques d'Orsay (LM-Orsay)
  • CNRS : UMR8628 – Université Paris XI - Paris Sud
  • Domain : Mathematics/Analysis of PDEs
  • Keywords : water waves – unstabilities – wave equations – spectral theory – non-linear models
 
  • hal-00429739, version 1
  • http://hal.archives-ouvertes.fr/hal-00429739
  • oai:hal.archives-ouvertes.fr:hal-00429739
  • From: - Département Mathématiques Orsay <>
  • Submitted on: Wednesday, 4 November 2009 11:00:51
  • Updated on: Wednesday, 4 November 2009 15:48:54