Calculation Of Hydrodynamic Coefficients Of The Floating Body Based On Rankine-kelvin Source Method In Two Subdomains

The simple Rankine Green function can be easily implemented, but it has some disadvantages such as a large number of panels, which represents the free surface. In this work,the fluid domain is divided into two subdomains by a control surface,an infinite cylinder. The velocity and the normal derivaties on the surface are represented by a series of Laguerre functions using Laguerre polynomials and Fourier series.This surface separates the problem into two problems: 1) the internal one in which the floating body is of any form,the Green function is Rankine source Green function, the freesurface is finite and all normal derivatives of velocity potentials ? are known on the floating body hull and the control surface as the solution of external problem; 2) the external one in which the shape of control surface is known, infinite cylinder, and the velocity is assumed to be known. The combination of these two methods keeps their advantages and brings two important benefits: On the one hand, area to be discretized becomes smaller, on the other hand, the calculation of the Green function for floating body motion may be done only once for large set of the different ships for the one particular velocity U. Main contents are as follows:Firstly, according to general method of three dimensional hydrodynamic coefficients in frequency, the solving conditions based on the Kelvin source method in external domain and Rankine source method in internal domain are given separately.Secondly, the variation of velocity and the normal derivaties can be represented by a series of Laguerre functions using Laguerre polynomials and Fourier series on the surface. The proof of uniform convergence is given in mathematics. Numerical approxim -ation of diffraction waves on infinite cylinder surface based on orthogonal function are compared to analytical solutions to verify correctness.Subquently, numerical solution of multiple integral especially for singular integral which contains Green function and its normal derivaties is given.Lastly, added mass and damping coeficients are calculated based on multi-domain Rankine-Kelvin method and numerical results are compared with analytical results of a floating hemisphere of heave and surge to verify the correctness and accuracy.