Approximation of Higher-Order Derivatives of the Frequency Domain Free Surface Green Function

2015 ◽  
Author(s):  
Yuyun Shi ◽  
Hui Li ◽  
Zhifu Li ◽  
Huilong Ren
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Frequency Domain ◽  
Higher Order ◽  
Boundary Element Methods ◽  
Source Distribution ◽  
Chebyshev Series ◽  
Surface Green Function ◽  
The Green Function ◽  
Derivatives Of

The higher-order derivatives of the free-surface Green Function are critically important in three-dimensional frequency-domain boundary element methods using mixed dipole-source distribution. To improve the accuracy and efficiency of numerical schemes, the computing domain is divided into five areas. Derivatives in four areas are calculated analytically since the Green function is defined analytically. The 5th area is divided into a number of sub-areas in which truncated Double Chebyshev series are used to approximate the Green function. Unlike the usual way in which the derivatives of Green function are obtained by differentiating the series, we re-approximate the derivatives by new Chebyshev series with new coefficients. Numerical results show that the new series are more accurate, in particular, second order derivatives.

Influence of the Waterline Integral on the Solution of the Frequency-Domain Forward-Speed Radiation-Diffraction Problem of a Ship Advancing in Waves

2014 ◽  
Author(s):  
D. C. Hong ◽  
S. Y. Hong ◽  
G. J. Lee ◽  
M. S. Shin
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Green Function ◽  
Frequency Domain ◽  
Surface Condition ◽  
Numerical Results ◽  
Forward Speed ◽  
Line Integral ◽  
Free Surface Condition ◽  
Surface Green Function

The radiation-diffraction potential of a ship advancing in waves is studied using the three-dimensional frequency-domain forward-speed free-surface Green function (Brard 1948) and the forward-speed Green integral equation (Hong 2000). Numerical solutions are obtained by making use of a second-order inner collocation boundary element method which makes it possible to take account of the line integral along the waterline in a rigorous manner (Hong et al. 2008). The present forward-speed Green integral equation includes not only the usual free surface condition for the potential but also the adjoint free surface condition for the forward-speed free-surface Green function as indicated by Brard (1972). Comparison of the present numerical results of the heave-heave wave damping coefficients and the experimental results for the Wigley ship models I, II and III (Journee 1992) has been presented. These coefficients are compared with those calculated without taking into account of the line integral along the waterline in order to show the forward speed effect represented by the waterline integral when it is properly included in the free-surface Green integral equation. Comparison of the present numerical results and the equivalent time-domain results (Hong et al. 2013) has also been presented.

Numerical Study of the Ship Motion in Waves Using the Three-Dimensional Time-Domain Forward-Speed Free-Surface Green Function and a Second-Order Boundary Element Method

2008 ◽  
Author(s):  
D. C. Hong ◽  
S. Y. Hong ◽  
H. G. Sung
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Green Function ◽  
Time Domain ◽  
Time Derivative ◽  
Three Dimensional ◽  
Forward Speed ◽  
Surface Green Function ◽  
The Green Function ◽  
The Time Domain

The radiation and diffraction potentials of a ship advancing in waves are calculated in the time-domain using the three-dimensional time-domain forward-speed free-surface Green function and the Green integral equation on the basis of the Neumann-Kelvin linear wave hypothesis. The Green function approximated by Newman for large time is used together with the Green function by Lamb for small time. The time-domain diffraction problem is solved for the time derivative of the potential by using the time derivative of the impulsive incident wave potential represented by using the complementary complex error function. The integral equation for the potential is discretized according to a second-order boundary element method where the collocation points are located inside the panel. It makes it possible to take account of the line integral along the waterline in a rigorous manner. The six-degree-of-freedom motion and memory functions as well as the diffraction impulse response functions of a hemisphere and the Wigley seakeeping model are presented for various Froude numbers. Comparisons of the wave damping and exciting force and moment coefficients for zero forward speed, calculated by using the Fourier transforms of the time-domain results and the frequency-domain coefficients calculated by using the improved Green integral equation which is free of the irregular frequencies, have been shown to be satisfactory. The wave damping coefficients for non-zero forward speed, calculated by using Fourier transforming of the present time-domain results have also been compared to the experimental results and agreement between them has been shown to be good. A simulation of coupled heave-pitch motion of the Wigley seakeeping model advancing in regular head waves of unit amplitude has been carried out.

Lifting Effects for Wave Resistance or Sea-Keeping Calculations

2002 ◽  
Author(s):  
Jean Philippe Boin ◽  
Michel Guilbaud ◽  
Malick Ba
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Surface Condition ◽  
The Body ◽  
Source Distribution ◽  
Diffraction Radiation ◽  
First Order ◽  
Wigley Hull ◽  
The Green Function ◽  
Sailing Boat

We present the introduction of lifting effects in a code of calculation [1–3] based on a first order panel method using the diffraction-radiation with forward speed Green function satisfying a linearised free-surface condition and the radiation one. A mixed formulation has been used with a source distribution on the hull and a doublet one on the plane of symmetry and the wake of lifting parts of the body, leading to an integral equation derived from the 3 rd Green identity. The Green function and its derivatives are not computed but are directly integrated on elementary panels, segments or semi-infinite strips. Results are presented for semi-submerged ellipsoid, rectangular surface-piercing bodies, Wigley hull, Series 60 ship, sailing boat and military 5415 hull. Global forces, moments but also free surface elevations are compared with the results of other methods and with measurements, either in steady or in unsteady flows in the frequency domain.

Free Surface Green Function Research Based on Cloud Computing for Ship Movement on the Water

2013 ◽  
Vol 344 ◽  
pp. 27-30
Author(s):  
Cong Zhang ◽  
Xin Wang ◽  
Jie Zhao ◽  
She Sheng Zhang
Keyword(s):  
Cloud Computing ◽  
Free Surface ◽  
Green Function ◽  
Point Source ◽  
Calculation Procedure ◽  
Green Functions ◽  
Two Dimensional ◽  
Surface Green Function ◽  
Cloud Computation ◽  
Control Equation

In order to easy use Green function on cloud computation, the author consider control equation of point source with free surface, and discuss the representation of Green function on cloud computation, and then propose the discrete calculation expression as well as the calculation procedure. Finally, the two-dimensional graphics of the Green functions real and imaginary parts are plotted.

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