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Numerical simulations of surface water waves
by
Philippe Guyenne
Department of Mathematical Sciences, University of Delaware
We present numerical simulations of surface water waves in 2D and 3D. The numerical method is based on potential flow theory and on a Hamiltonian formulation for water waves. The problem is reduced to a lower-dimensional system involving boundary variables alone. This is accomplished by introducing the Dirichlet-Neumann operator (DNO) which gives the normal fluid velocity at the free surface. A Taylor series expansion of the DNO in powers of the surface elevation is proposed. We develop an efficient and accurate spectral method using the fast Fourier transform to evaluate numerically the DNO and to solve the equations of motion. Tests and validation of the model will be presented. This is joint work with W. Craig (McMaster University), C. Sulem (University of Toronto) and L. Xu (University of Delaware).
Date received: January 23, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavk-84.