An implicit-explicit finite volume scheme for the fully nonlinear Serre system of equations

Denys Dutykh (1) , Didier Clamond (2) , Paul Milewski (3) , Dimitrios Mitsotakis (4)

1 LAMA - Laboratoire de Mathématiques
2 JAD - Laboratoire Jean Alexandre Dieudonné
3 University of Wisconsin-Madison
4 IMA - Institute for Mathematics and its Applications

After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate numerical scheme to solve these equations based on the finite volume method. The numerical discretization is validated by comparisons with analytical, experimental data or other numerical solutions obtained by a highly accurate pseudo-spectral method.

Mots clés: Serre equations; finite volumes; UNO scheme; IMEX scheme; spectral methods

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Formation de Structures et Solitons [nlin.PS]; Dynamique des Fluides [physics.flu-dyn]; Physique Numérique [physics.comp-ph]; Physique Atmosphérique et Océanique [physics.ao-ph]

Denys Dutykh, Didier Clamond, Paul Milewski, Dimitrios Mitsotakis. An implicit-explicit finite volume scheme for the fully nonlinear Serre system of equations. 2011. ⟨hal-00587994v2⟩