Progress in fully nonlinear potential flow modeling of 3D extreme ocean waves

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This article reviews recent research progress by the authors and coworkers, in the application of three-dimensional (3D) Numerical Wave Tanks (NWT), based on Fully Nonlinear Potential Flow theory (FNPF), to the modeling of extreme, overturning, ocean waves and of their properties, in both deep and shallow water. Details of the model equations and numerical methods are presented. Applications are then presented for the shoaling and 3D overturning in shallow water of solitary waves over a sloping ridge, for the generation of extreme deep and intermediate water waves, often referred to as “rogue” waves, by directional energy focusing, for the generation of tsunamis by solid underwater landslides, and for the generation of surface waves by a moving pressure disturbance. In all cases, physical and numerical aspects are presented and properties of generated waves are discussed at the breaking point. Aspects of numerical methods influencing the accuracy and the efficiency of the NWT solution are detailed in the article. Specifically, the 3D-NWT equations are expressed in a mixed Eulerian-Lagrangian formulation (or pseudo-Lagrangian in one case) and solved based on a higher-order Boundary Element Method (BEM), for the spatial solution, and using explicit higher-order Taylor series expansions for the time integration. Direct and iterative solutions of the governing equations are discussed, as well as results of a recent application of the Fast Multipole Algorithm. Detailed aspects of the model such as the treatment of surface piercing solid boundaries are discussed as well.

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Advances In Numerical Simulation Of Nonlinear Water Waves