Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank

• Published in: Volume 9: Odd M. Faltinsen Honoring Symposium on Marine Hydrodynamics
• Main Authors: Christiansen, Torben B., Bingham, Harry B., Engsig-Karup, Allan P., Ducrozet, Guillaume, Ferrant, Pierre
• Other Authors: Danmarks Tekniske Universitet = Technical University of Denmark (DTU), Laboratoire de recherche en Hydrodynamique, Énergétique et Environnement Atmosphérique (LHEEA), École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2013
• Subjects: Waves; [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]; Laplace; Arctic
• Online Access: https://hal.science/hal-01160630; https://doi.org/10.1115/OMAE2013-10861

International audience 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 Dirichlet-to-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.