TECHNICAL PAPERS
Sep 1, 2006

Finite-Element Computation of Wave-Structure Interaction between Steep Stokes Waves and Vertical Cylinders

Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 132, Issue 5

Abstract

The diffraction of highly nonlinear Stokes waves by vertical cylinders of circular cross section is numerically simulated in the time domain. A finite-element method, based on Hamilton’s principle, is used to discretize the fluid domain. The Stokes waves, input at the numerical wave maker, are obtained numerically from the two-dimensional steady solution of the finite element model. A new matching scheme is developed to match the two-dimensional wave at the far field and the three-dimensional diffracted wave in the near field. The method developed here can easily be extended to the diffraction of irregular, nonlinear waves. Numerical examples are presented for the diffraction of Stokes waves with various steepnesses by single and multiple circular cylinders. The wave elevation and runup on the cylinder are calculated and compared with the available theoretical and experimental results.

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Acknowledgments

The second writer is grateful for financial support from both the development of design technology of VLFS funded by MOMAF and the basic research and development program supported by Korea Research Council of Public Science and Technology.

References

Bai, K. J., Kim, J. W., and Lee, H. G. (1992). “A localized finite-element method for nonlinear free surface wave problems.” Proc., 19th Symp. on naval hydrodynamics, Seoul, Korea, 113–139.
Bai, K. J., and Han, J. H. (1994). “A localized finite-element method for the nonlinear steady waves due to a two-dimensional hydrofoil.” J. Ship Res., 38(1), 42–51.
Bai, K. J., and Kim, J. W. (1995). “A finite-element method for free-surface flow problems.” Theor Appl. Mech., 1(1), 1–27.
Bai, K. J., Kyoung, J. H., and Kim, J. W. (2003). “Numerical computations for a nonlinear free surface problem in shallow water.” J. Offshore Mech. Arct. Eng., 125(1), 33–40.
Buchmann, B., Skourup, J., and Cheung, K. F. (1997). “Runup on a structure due to waves and current.” Proc., 7th Int. Offshore and Polar Engineering Conf., Honolulu.
Clement, A. H. (1999). “Benchmark test cases for numerical wave absorption.” 1st Workshop of ISOPE Numerical Wave Tank Group, Montreal, Proc., 9th Int. Offshore and Polar Engineering Conf., Vol. 3, Brest, France, 266–289.
Cokelet, E. D. (1977). “Steep gravity waves in water of arbitrary uniform depth.” Philos. Trans. R. Soc. London, Ser. A, 286, 183–230.
Dommermuth, D. G., and Yue, D. K. P. (1986). “Study of nonlinear axisymmetric body-wave interaction.” Proc., 16th Symp. Naval Hydrodynamics, Berkeley, Calif.
Ertekin, R. C., Webster, W. C., and Wehausen, J. V. (1986). “Waves caused by a moving disturbance in a shallow channel of finite width.” J. Fluid Mech., 169, 272–292.
Ferrant, P. (1998). “Runup on a cylinder due to waves and current: Potential flow solution with fully nonlinear boundary conditions.” Proc., 8th Int. Offshore and Polar Engineering Conf., Vol. 3, Montreal, 332–339.
Havelock, T. H. (1940). “The pressure of water waves upon a fixed obstacle.” Philos. Trans. R. Soc. London, Ser. A, 175, 409–421.
Kennedy, A. B., Kirby, J. T., Chen, Q., and Dalrymple, R. A. (2001). “Boussinesq-type equations with improved nonlinear performance.” Wave Motion, 33(3), 225–243.
Kim, J. W., and Bai, K. J. (1999). “A finite-element method for two-dimensional water wave problems.” Int. J. Numer. Methods Fluids, Vol. 30(1), 105–121.
Kim, J. W., Bai, K. J., Ertekin, R. C., and Webster, W. C. (2003). “A strongly-nonlinear model for water waves in water of variable depth—The irrotational Green–Naghdi model.” J. Offshore Mech. Arct. Eng., 125(1), 25–32.
Kim, J. W., Kyoung, J. H., Bai, K. J., and Ertekin, R. C. (2004). “A numerical study of nonlinear diffraction loads on floating bodies due to extreme transient waves.” Proc., 25th Symp. on Naval Hydrodynamics, Newfoundland and Labrador, St. John, Canada.
Kim, M. H., and Yue, D. K. P., (1989). “The second-order diffraction solution for an axisymmetric body. I: Monochromatic incident waves.” J. Fluid Mech., 200, 235–264.
Kim, Y. H., Kring, D. C., and Sclavounos, R. D. (1997). “Linear and nonlinear interactions of surface waves with bodies by a three-dimensional Rankine panel method.” Appl. Ocean. Res., 19, 235–249.
Kriebel, D. L. (1992). “Nonlinear wave interaction with a vertical circular cylinder. II: Wave runup.” Ocean Eng., 19(1), 75–99.
Longuett-Higgins, M. S., and Cokelet, E. D. (1976). “The deformation of steep surface waves on water. I: A numerical method of computation.” Philos. Trans. R. Soc. London, Ser. A 350, 1–26.
MacCamy, R. C., and Fuchs, R. A. (1954). “Wave forces on piles: A diffraction theory.” Beach Erosion Board Tech. Mem. No. 69.
Malenica, S., Eatock Taylor, R., and Huang, J. B. (1999). “Second-order water wave diffraction by an array of vertical cylinders.” J. Fluid Mech., 390, 349–373.
Malenica, S., and Molin, B. (1995). “Third harmonic wave diffraction by a vertical cylinder.” J. Fluid Mech., 302, 203–229.
Miles, J. W. (1977). “On Hamilton’s principle for surface waves.” J. Fluid Mech., 83, 153–158 (1978, pp. 797).
Miles, J. W. (1978). “On Hamilton’s principles for surface waves.” J. Fluid Mech., 85, 797.
Neill, D. R., and Ertekin, R. C. (1997). “Diffraction of solitary waves by a vertical cylinder: Green–Naghdi and Boussinesq equations.” Proc., 16th Int. Conf. on Offshore Mechanics and Arctic Eng., Vol. I-B, ASME, Yokohama, Japan, 63–71.
Serrin, J. (1959). “Mathematical principles of classical fluid mechanics.” Encyclopedia of physics, Vol. VIII/1, Springer, Berlin.
Swan, C., Taylor, P. H., and van Langen, H. (1997). “Observation of wave-structure interaction for a multilegged concrete platform.” Appl. Ocean. Res., 19, 309–327.
Tanizawa, K. (1996). “Long time fully nonlinear simulation of floating body motions with artificial damping zone.” J. Soc. Naval Architects Japan, 180, 311–319.
Yang, C., and Ertekin, R. C. (1992). “Numerical simulation of nonlinear wave diffraction by a vertical cylinder.” J. Offshore Mech. Arct. Eng., 114(1), 34–44.
Vinje, T., and Brevig, P. (1981). “Numerical simulation of breaking waves.” Adv. Water Resour., 4, 77–82.
Webster, W. C., and Kim, D. Y. (1990). “The dispersion of large-amplitude gravity waves in deep water.” Proc., 18th Symp. on Naval Hydrodynamics, Ann Arbor, Mich., 397–415.

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Go to Journal of Waterway, Port, Coastal, and Ocean Engineering
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 132Issue 5September 2006
Pages: 337 - 347

History

Received: Aug 11, 2003
Accepted: Jan 4, 2005
Published online: Sep 1, 2006
Published in print: Sep 2006

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Authors

Affiliations

J. W. Kim
Senior Engineer, American Bureau of Shipping, 16855 Northchase Dr., Houston, TX 77060-6008 (corresponding author). E-mail: [email protected]
J. H. Kyoung
Senior Researcher, Korea Ocean Research and Development Institute, Maritime and Ocean Engineering Research Institute, 171 Jang-dong Yuseong, Daejeon 305-343, Korea. E-mail: [email protected]
R. C. Ertekin
Professor, Dept. of Ocean and Resources Engineering, Univ. of Hawaii at Manoa, 2540 Dole St., Holmes Hall 402, Honolulu, HI 96822. E-mail: [email protected]
K. J. Bai
Professor, Dept. of Naval Architecture & Ocean Engineering, Seoul National Univ., Seoul, Korea. E-mail: [email protected]

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