DOI QR코드

DOI QR Code

An improved Rankine source panel method for three dimensional water wave problems

  • Feng, Aichun (Department of Civil and Environmental Engineering, National University of Singapore) ;
  • You, Yunxiang (State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University) ;
  • Cai, Huayang (Institute of Estuarine and Coastal Research, School of Marine Sciences, Sun Yat-sen University)
  • Received : 2017.08.16
  • Accepted : 2018.02.05
  • Published : 2019.01.31

Abstract

An improved three dimensional Rankine source method is developed to solve numerically water wave problems in time domain. The free surface and body surface are both represented by continuous panels rather than a discretization by isolated points. The integral of Rankine source 1/r on free surface panel is calculated analytically instead of numerical approximation. Due to the exact algorithm of Rankine source integral applied on the free surface and body surface, a space increment free surface source distribution method is developed and much smaller amount of source panels are required to cover the fluid domain surface than other numerical approximation methods. The proposed method shows a higher accuracy and efficiency compared to other numerical methods for various water wave problems.

Keywords

References

  1. Bai, W., Teng, B., 2013. Simulation of second-order wave interaction with fixed and floating structures in time domain. Ocean Eng. 74, 168-177. https://doi.org/10.1016/j.oceaneng.2013.07.014
  2. Bandyk, P., Beck, R., 2011. The acceleration potential in fluid-body interaction problems. J. Eng. Math. 70 (1), 147-163. https://doi.org/10.1007/s10665-010-9446-0
  3. Bandyk, P.J., 2009. A Body-exact Strip Theory Approach to Ship Motion Computations. Ph.D. thesis. University of Michigan.
  4. Beck, R., 1994. Time-domain computations for floating bodies. Appl. Ocean Res. 16 (5), 267-282. https://doi.org/10.1016/0141-1187(94)90016-7
  5. Beck, R.F., King, B., 1989. Time-domain analysis of wave exciting forces on floating bodies at zero forward speed. Appl. Ocean Res. 11 (1), 19-25. https://doi.org/10.1016/0141-1187(89)90003-5
  6. Cao, Y., Beck, R., Schultz, W., 1993. Numerical computations of two-dimensional solitary waves generated by moving disturbances. Int. J. Numer. Meth. Fluid. 17 (10), 905-920. https://doi.org/10.1002/fld.1650171006
  7. Cao, Y., Beck, R.F., 2016. Desingularized boundary integral equations and their applications in wave dynamics and wave-body interaction problems. J. Ocean Eng. Sci. 1 (1), 11-29. https://doi.org/10.1016/j.joes.2016.01.001
  8. Cao, Y., Schultz, W., Beck, R., 1990. Three-dimensional, unsteady computations of nonlinear waves caused by underwater disturbances. In: Proceedings of the 18th Symposium on Naval Hydrodynamics, vol.1, pp. 417-425.
  9. Cao, Y., Schultz, W., Beck, R., 1991. Three-dimensional desingularized boundary integral methods for potential problems. Int. J. Numer. Meth. Fluid. 12 (8), 785-803. https://doi.org/10.1002/fld.1650120807
  10. Chen, Z.-M., 2014. Regular wave integral approach to the prediction of hydrodynamic performance of submerged spheroid. Wave Motion 51 (2), 193-205. https://doi.org/10.1016/j.wavemoti.2013.06.005
  11. Das, S., Cheung, K.F., 2012. Scattered waves and motions of marine vessels advancing in a seaway. Wave Motion 49 (1), 181-197. https://doi.org/10.1016/j.wavemoti.2011.09.003
  12. Eatock Taylor, R., Chau, F., 1992. Wave diffraction theorysome developments in linear and nonlinear theory. J. Offshore Mech. Arctic Eng. 114 (3), 185-194. https://doi.org/10.1115/1.2919970
  13. Feng, A., Chen, Z.-M., Price, W., 2015. A continuous desingularized source distribution method describing wave-body interactions of a large amplitude oscillatory body. J. Offshore Mech. Arctic Eng. 137 (2).
  14. Gao, Z., Zou, Z., 2008. A NURBS-based high-order panel method for three-dimensional radiation and diffraction problems with forward speed. Ocean Eng. 35 (11), 1271-1282. https://doi.org/10.1016/j.oceaneng.2008.02.007
  15. Hess, J., Smith, A., 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
  16. 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
  17. Isaacson, M., Cheung, K.F., 1991. Second order wave diffraction around two-dimensional bodies by time-domain method. Appl. Ocean Res. 13 (4), 175-186. https://doi.org/10.1016/S0141-1187(05)80073-2
  18. Isaacson, M., Ng, J.Y., Cheung, K.F., 1993. Second-order wave radiation of three-dimensional bodies by time-domain method. International Journal of Offshore and Polar Engineering 3 (04).
  19. Israeli, M., Orszag, S.A., 1981. Approximation of radiation boundary conditions. J. Comput. Phys. 41 (1), 115-135. https://doi.org/10.1016/0021-9991(81)90082-6
  20. Kim, Y., Kring, D.C., Sclavounos, P.D., 1997. Linear and nonlinear interactions of surface waves with bodies by a three-dimensional rankine panel method. Appl. Ocean Res. 19 (5), 235-249. https://doi.org/10.1016/S0141-1187(97)00034-5
  21. Koo, W., Kim, M., 2004. Freely floating-body simulation by a 2D fully nonlinear numerical wave tank. Ocean Eng. 31 (16), 2011-2046. https://doi.org/10.1016/j.oceaneng.2004.05.003
  22. Koo, W., Kim, M., 2006. Numerical simulation of nonlinear wave and force generated by a wedge-shape wave maker. Ocean Eng. 33 (8), 983-1006. https://doi.org/10.1016/j.oceaneng.2005.09.002
  23. Koo, W., Kim, M., 2007. Fully nonlinear wave-body interactions with surface-piercing bodies. Ocean Eng. 34 (7), 1000-1012. https://doi.org/10.1016/j.oceaneng.2006.04.009
  24. Kouh, J., Suen, J., 2001. A 3D potential-based and desingularized high order panel method. Ocean Eng. 28 (11), 1499-1516. https://doi.org/10.1016/S0029-8018(00)00069-X
  25. Kring, D.C., Sclavounos, P.D., 1995. Numerical stability analysis for time-domain ship motion simulations. J. Ship Res. 39 (4), 313-320.
  26. Lamb, H., 1945. Hydrodynamics, sixth ed. Dover Publications, Inc, New York, pp. 59-60.
  27. Lee, C., Maniar, H., Newman, J., Zhu, X., 1996. Computations of wave loads using a b-spline panel method. In: Proceedings of the 21st Symposium on Naval Hydrodynamics, pp. 75-92.
  28. Lee, T., 1992. Nonlinear Radiation Problems for a Surface-piercing Body. Ph.D. thesis. University of Michigan.
  29. Lee, T., 2003. Fully nonlinear wave computations for arbitrary floating bodies using the delta method. Int. Hydrodyn. 15 (002).
  30. Maniar, H.D., 1995. A Three Dimensional Higher Order Panel Method Based on B-splines. Ph.D. thesis. Massachusetts Institute of Technology.
  31. Nakos, D., Sclavounos, P., 1990. On steady and unsteady ship wave patterns. J. Fluid Mech. 215, 263-288. https://doi.org/10.1017/S0022112090002646
  32. Nossen, J., Grue, J., Palm, E., 1991. Wave forces on three-dimensional floating bodies with small forward speed. J. Fluid Mech. 227, 135-160. https://doi.org/10.1017/S002211209100006X
  33. Sclavounos, P.D., Nakos, D.E., 1988. Stability analysis of panel methods for free-surface flows with forward speed. In: Proceeding of the 17th Symposium on Naval Hydrodynamics.
  34. Tanizawa, K., 1996. Long time fully nonlinear simulation of floating body motions with artificial damping zone. J. Soc. Nav. Archit. Jpn. 180, 311-319. https://doi.org/10.2534/jjasnaoe1968.1996.180_311
  35. Wang, L., Tang, H., Wu, Y., 2015. Simulation of waveebody interaction: a desingularized method coupled with acceleration potential. J. Fluid Struct. 52, 37-48. https://doi.org/10.1016/j.jfluidstructs.2014.08.009
  36. Wang, L., Tang, H., Wu, Y., 2016. Wave interaction with a surface-piercing body in water of finite depth: a parametric study. Eng. Appl. Comput. Fluid Mech. 10 (1), 512-528.
  37. Wehausen, J., Laitone, E., 1960. Surface Waves. Springer.
  38. Yonghui, L., Xinsen, L., 1988. Polar coordinate transformation approach for treatment of singular integrals in boundary element methods. Appl. Math. Mech. 9 (10), 959-967. https://doi.org/10.1007/BF02014602
  39. Zhang, X., Bandyk, P., Beck, R., 2010. Time-domain simulations of radiation and diffraction forces. J. Ship Res. 54 (2), 79-94. https://doi.org/10.5957/jsr.2010.54.2.79
  40. Zhang, X., Beck, R., 2007. Computations for large-amplitude two-dimensional body motions. J. Eng. Math. 58 (1), 177-189. https://doi.org/10.1007/s10665-006-9123-5
  41. Zhang, X., Beck, R., 2008. Three-dimensional large amplitude body motions in waves. J. Offshore Mech. Arctic Eng. 130 (4), 16-23.
  42. Zhang, X., Khoo, B., Lou, J., 2006. Wave propagation in a fully nonlinear numerical wave tank: a desingularized method. Ocean Eng. 33 (17), 2310-2331. https://doi.org/10.1016/j.oceaneng.2005.11.002

Cited by

  1. Development of a Three-Dimensional Fully Nonlinear Potential Numerical Wave Tank for a Heaving Buoy Wave Energy Converter vol.2019, 2019, https://doi.org/10.1155/2019/5163597
  2. Three dimensional numerical modelling for wave radiation problem under arbitrary seabed condition vol.230, 2019, https://doi.org/10.1016/j.oceaneng.2021.108885
  3. Numerical Investigation on Motion Responses of a Floating Hemisphere Over a Sloping Bottom vol.143, pp.5, 2019, https://doi.org/10.1115/1.4050423