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Summary: AN IMPLICIT DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR WATER WAVES
J. J. W. van der Vegt, V. R. Ambati, O. Bokhove
Department of Applied Mathematics, University of Twente, Enschede, The Netherlands
Email: j.j.w.vandervegt@math.utwente.nl
Abstract
We discuss a new higher order accurate discontinuous
Galerkin finite element method for non-linear free surface
gravity waves. The algorithm is based on an arbitrary
Lagrangian Eulerian description of the flow field using
deforming elements and a moving mesh, which makes it
possible to represent non-linear large amplitude waves.
The novel feature of the algorithm is a coupled treatment
of the free surface boundary condition and the domain
discretization, which improves numerical stability.
Introduction
The numerical simulation of free surface gravity waves
is an essential tool in the design and analysis of wave mo-
tion and its influence on fixed and floating structures. Free
surface gravity waves can be modelled at various levels of
sophistication, but for many applications it is sufficient to
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