• Journal of the Society of Naval Architects of Korea
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• v.30 no.1
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• pp.45-64
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• 1993

This paper dealt with the application of a numerical method developed by the authors using the matching method proposed in the previous paper on "The Nonlinear motions of cylinders(I)[16]", and Cauchy's theorem to the problems associated with hydrodynamic forces acting on a heaving cylinders translating in a calm water and also motions of cylinders in waves. In spectral method. body boundary condition in submerged case is satisfied exactly but one in floating case is not satisfied exactly. In the numerical code developed here, the boundary condition at the free-surface and body surface is satisfied exactly at its instaneous position. It is of interest to note that the present scheme could be applied to a free-surface-piercing body without experiencing a difficulty in the numerical convergence. The computed results are compared with other results([6], [12]).

• Journal of Ocean Engineering and Technology
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• v.32 no.6
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• pp.447-457
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• 2018

In this study, a two-dimensional fully nonlinear transient wave numerical tank was developed using a desingularized indirect boundary integral equation method. The desingularized indirect boundary integral equation method is simpler and faster than the conventional boundary element method because special treatment is not required to compute the boundary integral. Numerical simulations were carried out in the time domain using the fourth order Runge-Kutta method. A mixed Eulerian-Lagrangian approach was adapted to reconstruct the free surface at each time step. A numerical damping zone was used to minimize the reflective wave in the downstream region. The interpolating method of a Gaussian radial basis function-type artificial neural network was used to calculate the gradient of the free surface elevation without element connectivity. The desingularized indirect boundary integral equation using an isolated point source and radial basis function has no need for information about the element connectivity and is a meshless method that is numerically more flexible. In order to validate the accuracy of the numerical wave tank based on the desingularized indirect boundary integral equation method and meshless technique, several numerical simulations were carried out. First, a comparison with numerical results according to the type of desingularized source was carried out and confirmed that continuous line sources can be replaced by simply isolated sources. In addition, a propagation simulation of a $2^{nd}$-order Stokes wave was carried out and compared with an analytical solution. Finally, simulations of propagating waves in shallow water and propagating waves over a submerged bar were also carried and compared with published data.