International Journal of Naval Architecture and Ocean Engineering

The Society of Naval Architects of Korea (대한조선학회)
권호 표지
DOI QR코드

DOI QR Code

Accuracy evaluation of 3D time-domain Green function in infinite depth

  • Zhang, Teng (State Key Laboratory of Structural Analysis for Industrial Equipment, School of Naval Architecture Engineering, Dalian University of Technology) ;
  • Zhou, Bo (State Key Laboratory of Structural Analysis for Industrial Equipment, School of Naval Architecture Engineering, Dalian University of Technology) ;
  • Li, Zhiqing (State Key Laboratory of Structural Analysis for Industrial Equipment, School of Naval Architecture Engineering, Dalian University of Technology) ;
  • Han, Xiaoshuang (Marine Engineering College, Dalian Maritime University) ;
  • Gho, Wie Min (Maritime Production research Pte. Ltd)
  • Received : 2020.08.17
  • Accepted : 2020.11.30
  • Published : 2021.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

An accurate evaluation of three-dimensional (3D) Time-Domain Green Function (TDGF) in infinite water depth is essential for ship's hydrodynamic analysis. Various numerical algorithms based on the TDGF properties are considered, including the ascending series expansion at small time parameter, the asymptotic expansion at large time parameter and the Taylor series expansion combines with ordinary differential equation for the time domain analysis. An efficient method (referred as "Present Method") for a better accuracy evaluation of TDGF has been proposed. The numerical results generated from precise integration method and analytical solution of Shan et al. (2019) revealed that the "Present method" provides a better solution in the computational domain. The comparison of the heave hydrodynamic coefficients in solving the radiation problem of a hemisphere at zero speed between the "Present method" and the analytical solutions proposed by Hulme (1982) showed that the difference of result is small, less than 3%.

Keywords

Acknowledgement

This research is supported by the LiaoNing Revitalization Talents Program (No. XLYC1807190, XLYC1908027); National Natural Science Foundation of China (No. 52071059).

References

  1. Beck, R., Liapis, S., 1987. Transient motions of floating bodies at zero forward speed. J. Ship Res. 31 (3), 164-176. https://doi.org/10.5957/jsr.1987.31.3.164
  2. Bingham, H.B., 2016. A note on the relative efficiency of methods for computing the transient free-surface Green function[J]. Ocean. Eng. 120, 15-20. https://doi.org/10.1016/j.oceaneng.2016.05.020
  3. Chuang, J.M., Qiu, W., Peng, H., 2007. On the evaluation of the time-domain Green function. Ocean. Eng. 34, 962-969. https://doi.org/10.1016/j.oceaneng.2006.05.010
  4. Clement, A.H., 1998. An ordinary differential equation for green function of time-domain free-surface hydrodynamics. J. Eng. Math. 33 (2), 201-217, 1998. https://doi.org/10.1023/A:1004376504969
  5. Datta, R., Rodrigues, J.M., Soares, C.G., 2011. Study of the motions of fishing vessels by a time domain panel method. Ocean. Eng. 38 (5), 782-792. https://doi.org/10.1016/j.oceaneng.2011.02.002
  6. Duan, W.Y., Dai, Y.S., 2001. New derivation of ordinary differential equations for transient free-surface Green functions. China Ocean Eng. 4, 499-507.
  7. Hess, J.L., Smith, A.M.O., 1964. Calculation of non-lifting potential flow about arbitrary three-dimensional bodies. J. Ship Res. 8 (2), 22-44. https://doi.org/10.5957/jsr.1964.8.4.22
  8. Huang, D.B., 1992. Approximation of time-domain free surface function and its spatial derivatives. Shipbuilding of China 2, 16-25.
  9. Hulme, A., 1982. The wave forces acting on a floating hemisphere undergoing forced periodic oscillations. J. Fluid Mech. 121, 443-463. https://doi.org/10.1017/S0022112082001980
  10. King, B.W., 1987. Time Domain Analysis of Wave Exciting Forces on Ships and Bodies. Ph.D. Thesis. The University of Michigan, Ann Arbor, Michigan.
  11. Liapis, S.J., 1986. Time Domain Analysis of Ship Motions. Ph.D. Thesis. The University of Michigan, Ann Arbor.
  12. Li, Z.F., Ren, H.L., Tong, X.W., Li, H., 2015. A precise computation method of transient free surface Green function. Ocean. Eng. 105, 318-326. https://doi.org/10.1016/j.oceaneng.2015.06.048
  13. Newman, J.N., 1992. The approximation of free-surface Green functions. In: Martin, P.A., Wickham, G.R. (Eds.), Wave Asymptotics. Cambridge University Press, Cambridge, UK, pp. 107-135.
  14. Shan, P.H., Wang, Y.H., Wang, F.H., Wu, J.M., Zhu, R.C., 2019. An efficient algorithm with new residual functions for the transient free surface green function in infinite depth. Ocean. Eng. 178, 435-441. https://doi.org/10.1016/j.oceaneng.2019.03.003
  15. Shen, L., Zhu, R.C., Miao, G.P., Liu, Y.Z., 2007. A practical numerical method for deep water time domain in Green function. Chinese Journal of Hydrodynamics 3, 380-386.
  16. Singh, S.P., Sen, D., 2007. A comparative linear and nonlinear ship motion study using 3-D time domain methods. Ocean. Eng. 34 (13), 1863-1881. https://doi.org/10.1016/j.oceaneng.2006.10.016
  17. Sun, L., 2009. A Study of Ship-Generated Waves and its Effects on Structures. Ph.D.Thesis. The Dalian University of Technology, Dalian.
  18. Sun, W., Ren, H.L., 2018. Ship motions with forward speed by time-domain Green function method. Chinese Journal of Hydrodynamics 33 (2), 216-222.
  19. Tong, X.L., 2013. Three Dimensional Time Domain Hybrid Method for Ship and Marine Structure Motions. Ph.D.Thesis. Harbin Engineering University, Harbin.
  20. Wehausen, J.V., Laitone, E.V., 1960. Surface Waves. Encyclopedia of Physics, Vol. IX/Fluid Dynamics III. Springer-Verlag, Berlin, pp. 446-778.
  21. Zhang, G.Y., Wang, S.Q., Sui, Z.X., Sun, L., Zhang, Z.Q., Zong, Z., 2019. Coupling of SPH with smoothed point interpolation method for violent fluid structure interaction problems. Eng. Anal. Bound. Elem. 103, 1-10. https://doi.org/10.1016/j.enganabound.2019.02.010
  22. Zhong, W.X., 2004. On precise integration method. J. Comput. Appl. Math. 163, 59-78. https://doi.org/10.1016/j.cam.2003.08.053