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Applicability of the method of fundamental solutions to 3-D wave–body interaction with fully nonlinear free surface

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Abstract

A numerical model for three-dimensional fully nonlinear free-surface waves is developed by applying a boundary-type meshless approach with a leap-frog time-marching scheme. Adopting Gaussian Radial Basis Functions to fit the free surface, a non-iterative approach to discretize the nonlinear free-surface boundary is formulated. Using the fundamental solutions of the Laplace equation as the solution form of the velocity potential, free-surface wave problems can be solved by collocations at only a few boundary points since the governing equation is automatically satisfied. The accuracy of the present method is verified by comparing the simulated propagation of a solitary wave with an exact solution. The applicability of the present model is illustrated by applying it to the problem of a solitary wave running up on a vertical surface-piercing cylinder and the problem of wave generation in infinite water depth by a submerged moving object.

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  1. Department of Civil Engineering, National Taiwan University, 1 Roosevelt Rd., Sec. 4, Taipei City, 10617, Taiwan

    Nan-Jing Wu & Ting-Kuei Tsay

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  1. Nan-Jing Wu
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  2. Ting-Kuei Tsay
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Correspondence to Ting-Kuei Tsay.

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Wu, NJ., Tsay, TK. Applicability of the method of fundamental solutions to 3-D wave–body interaction with fully nonlinear free surface. J Eng Math 63, 61–78 (2009). https://doi.org/10.1007/s10665-008-9250-2

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  • DOI: https://doi.org/10.1007/s10665-008-9250-2

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