Preprint 1996-023

A finite element method for fully nonlinear water waves

Abstract: We introduce a numerical method for a mathematical model of fully nonlinear water waves. The method is based on a transformation of the dynamic water volume onto a fixed domain, thus regridding at each time step is avoided. The transformation introduces an elliptic boundary value problem which is solved by a preconditioned conjugate gradient method. Numerical experiments are presented and they show nice convergence properties of the iterative solver as well as convergence of the entire solution towards a reference solution computed by another scheme.

Paper:

Available as PostScript

Title:

A finite element method for fully nonlinear water waves

Author(s):

Xing Cai , <Xing.Cai@si.sintef.no>

Hans Petter Langtangen , <hpl@math.uio.no>

Bjørn Fredrik Nielsen, <bjornn@ifi.uio.no>

Aslak Tveito , <aslak@ifi.uio.no>

Publishing information:

Preprint at the Department of Informatics, University of Oslo

Comments:

Some snapshots taken from the computer simulation can be viewed at this WWW site.

Submitted by:

<Xing.Cai@si.sintef.no> August 12 1996.