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Variational Space-time (Dis)continuous Galerkin Method for Linear Free Surface Waves

Summary: Variational Space-time (Dis)continuous Galerkin
Method for Linear Free Surface Waves
V.R. Ambati, J.J.W. van der Vegt, and O. Bokhove
v.r.ambati@math.utwente.nl, o.bokhove@math.utwente.nl and
Numerical Analysis and Computational Mechanics Group
Department of Applied Mathematics, University of Twente
P.O. Box 217, Enschede, The Netherlands.
March 5, 2008
A new variational (dis)continuous Galerkin finite element method is presented for linear free
surface gravity water wave equations. In this method, the space-time finite element discretiza-
tion is based on a discrete variational formulation analogous to a version of Luke's variational
principle. The finite element discretization results into a linear algebraic system of equations
with a symmetric and compact stencil. These equations have been solved using the PETSc
package, in which a block sparse matrix storage routine is used to build the matrix and an
efficient conjugate gradient solver to solve the equations. The finite element scheme is verified
against exact solutions: linear free surface waves in a periodic domain and ones generated by a
harmonic wave maker in a rectangular wave basin. We found that the variational scheme has
no dissipation and minimal dispersion errors in the wave propagation, and that the numerical


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering