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 Titel: An efficient flexible-order model for coastal and ocean water waves Type: Conference abstract for conferenceConference abstract for conference Person(er): Forfatter:  Engsig-Karup, Allan Peter (Cwisno: 22171) Technical University of Denmark Email: --- Forfatter:  Bingham, Harry B. (Cwisno: 6371) Technical University of Denmark Email: --- Forfatter:  Lindberg, Ole (Cwisno: 17659) Technical University of Denmark Email: --- Uddrag: Current work are directed toward the development of an improved numerical 3D model for fully nonlinear potential water waves over arbitrary depths. The model is high-order accurate, robust and efficient for large-scale problems, and support will be included for flexibility in the description of structures. The mathemathical equations for potential waves in the physical domain is transformed through $\sigma$-mapping(s) to a time-invariant boundary-fitted domain which then becomes a basis for an efficient solution strategy. The improved 3D numerical model is based on a finite difference method as in the original works \cite{LiFleming1997,BinghamZhang2007}. The new and improved approach employs a GMRES solver with multigrid preconditioning to achieve optimal scaling of the overall solution effort, i.e., directly with $n$ the total number of grid points. A robust method is achieved through a special treatment of the boundary conditions along solid boundaries, and is necessary for a robust multigrid preconditioning strategy. Full details and other aspects of the 3D solution will appear in \cite{EngsigKarupBinghamLindberg2008}. At the symposium, we will present examples demonstrating the fundamental properties of the numerical model together with the latests achievements. Publiceret: Fil(er): Præsenteret ved: First American Academy of Mechanics Conference, New Orleans
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