TY - JOUR

T1 - A Hamiltonian approach to fairly low and fairly long gravity waves

AU - Veen, W.A. van der

AU - Wubs, F.W.

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi
Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)

PY - 1995/7

Y1 - 1995/7

N2 - The propagation of nonlinear dispersive gravity waves in an inviscid irrotational fluid can be described by a Hamiltonian system. The canonical equations contain a boundary integral which is computationally expensive. However, for fairly low and fairly long waves an approximation can be made that gives rise to the solution of computationally more attractive Helmholtz-type equations. In an earlier attempt, canonical equations were derived that are stable for all wavenumbers. However, two Helmholtz-type equations need to be solved per right-hand side evaluation. In this paper, canonical equations are presented with the same qualities, but now only once per right-hand side evaluation a Helmholz-type equation needs to be solved, which is optimal.

AB - The propagation of nonlinear dispersive gravity waves in an inviscid irrotational fluid can be described by a Hamiltonian system. The canonical equations contain a boundary integral which is computationally expensive. However, for fairly low and fairly long waves an approximation can be made that gives rise to the solution of computationally more attractive Helmholtz-type equations. In an earlier attempt, canonical equations were derived that are stable for all wavenumbers. However, two Helmholtz-type equations need to be solved per right-hand side evaluation. In this paper, canonical equations are presented with the same qualities, but now only once per right-hand side evaluation a Helmholz-type equation needs to be solved, which is optimal.

M3 - Article

VL - 29

SP - 329

EP - 345

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 4

ER -