Efficient computation of capillary-gravity generalized solitary waves

Denys Dutykh (1, 2, 3) , Didier Clamond (4) , Angel Duran (5)

1 LAMA - Laboratoire de Mathématiques
2 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
3 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
4 LJAD - Laboratoire Jean Alexandre Dieudonné
5 MA - Departamento de Matemática Aplicada [Valladolid]

This paper is devoted to the computation of capillary-gravity solitary waves of the irrotational incompressible Euler equations with free surface. The numerical study is a continuation of a previous work in several points: an alternative formulation of the Babenko-type equation for the wave profiles, a detailed description of both the numerical resolution and the analysis of the internal flow structure under a solitary wave. The numerical code used in this study is provided in open source for those interested readers.

Mots clés: generalised solitary waves; capillary-gravity waves; Euler equations; Solitary surface waves

Domaines: Mécanique des fluides [physics.class-ph]; Formation de Structures et Solitons [nlin.PS]; Equations aux dérivées partielles [math.AP]; Systèmes Solubles et Intégrables [nlin.SI]; Océan, Atmosphère; Milieux fluides et réactifs; Physique Numérique [physics.comp-ph]; Analyse numérique [math.NA]; Physique Atmosphérique et Océanique [physics.ao-ph]; Dynamique des Fluides [physics.flu-dyn]; Physique Générale [physics.gen-ph]

Denys Dutykh, Didier Clamond, Angel Duran. Efficient computation of capillary-gravity generalized solitary waves. Wave Motion, 2016, 65, pp.1-16. ⟨10.1016/j.wavemoti.2016.04.007⟩. ⟨hal-01218989v2⟩