Christiansen, Torben5; Bingham, Harry B.3; Engsig-Karup, Allan Peter6; Ducrozet, Guillaume8; Ferrant, Pierre8
1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Scientific Computing, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Department of Mechanical Engineering, Technical University of Denmark4 Fluid Mechanics, Coastal and Maritime Engineering, Department of Mechanical Engineering, Technical University of Denmark5 Department of Informatics and Mathematical Modeling, Technical University of Denmark6 Center for Energy Resources Engineering, Center, Technical University of Denmark7 Ecole Centrale de Nantes8 Ecole Centrale de Nantes
A new hybrid-spectral solution strategy is proposed for the simulation of the fully nonlinear free surface equations based on potential flow theory. A Fourier collocation method is adopted horisontally for the discretization of the free surface equations. This is combined with a modal Chebyshev Tau method in the vertical for the discretization of the Laplace equation in the fluid domain, which yields a sparse and spectrally accurate Dirichletto-Neumann operator. The Laplace problem is solved with an efficient Defect Correction method preconditioned with a spectral discretization of the linearised wave problem, ensuring fast convergence and optimal scaling with the problem size. Preliminary results for very nonlinear waves show expected convergence rates and a clear advantage of using spectral schemes.
32nd International Conference on Ocean, Offshore and Arctic Engineering, 2013
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32nd International Conference on Ocean, Offshore and Arctic Engineering (OMAE 2013)International Conference on Ocean, Offshore and Arctic Engineering