An efficient flexible-order model for coastal and ocean water waves

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    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.
    Original languageEnglish
    Publication date2008
    Publication statusPublished - 2008
    EventFirst American Academy of Mechanics Conference - New Orleans
    Duration: 1 Jan 2008 → …
    Conference number: 1


    ConferenceFirst American Academy of Mechanics Conference
    CityNew Orleans
    Period01/01/2008 → …


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