2016
Multi-symplectic structure of fully-nonlinear weakly-dispersive internal gravity waves
JJ. Phys. A: Math. Theor.
D. Clamond and D. Dutykh
J. Phys. A: Math. Theor. 49(31LT01): 31LT01 (2016)
Open Access
Abstract
In this short communication we present the multi-symplectic structure for the two-layer Serre-Green-Naghdi equations describing the evolution of large amplitude internal gravity long waves. We consider only a two-layer stratification with rigid bottom and lid for simplicity, generalisations to several layers being straightforward. This multi-symplectic formulation allows the application of various multi-symplectic integrators (such as Euler or Preissman box schemes) that preserve exactly the multi-symplecticity at the discrete level.
Keywords
fully-nonlineartwo-layer flowmulti-symplectic integratorstwo-layer stratificationEuler schemeinternal gravity wavesinternal wavesweakly-dispersiveSerre-Green-Naghdi equationsPreissman box schemeGreen-Naghdi equationsmulti-symplectic structurelong wavesrigid bottom and lid
Bibliographic record
BibTeX Citation
@article{Clamond2016multisymplecticstructure,
author = {Clamond, D. and Dutykh, D.},
title = {Multi-symplectic structure of fully-nonlinear weakly-dispersive internal gravity waves},
journal = {J. Phys. A: Math. Theor.},
year = {2016},
volume = {49},
number = {31LT01},
pages = {31LT01},
doi = {10.1088/1751-8113/49/31/31LT01},
abstract = {In this short communication we present the multi-symplectic structure for the two-layer Serre-Green-Naghdi equations describing the evolution of large amplitude internal gravity long waves. We consider only a two-layer stratification with rigid bottom and lid for simplicity, generalisations to several layers being straightforward. This multi-symplectic formulation allows the application of various multi-symplectic integrators (such as Euler or Preissman box schemes) that preserve exactly the multi-symplecticity at the discrete level.},
keywords = {fully-nonlinear, two-layer flow, multi-symplectic integrators, two-layer stratification, Euler scheme, internal gravity waves, internal waves, weakly-dispersive, Serre-Green-Naghdi equations, Preissman box scheme, Green-Naghdi equations, multi-symplectic structure, long waves, rigid bottom and lid}
}