Scaled Boundary FEM Model for Interaction of Short-Crested Waves with a Concentric Porous Cylindrical Structure
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 135, Issue 5
Abstract
This paper describes the development of an efficient scaled boundary finite-element model (FEM) for the simulation of short-crested wave interaction with a concentric porous cylindrical structure. By weakening the governing differential equation in the circumferential direction, the SBFEM is able to solve analytically the weakened equation in the radial direction. Only the cylinder boundary on the circumference of the exterior porous cylinder is discretized with curved surface finite elements, while a complete analytical representation is obtained for the radial differential equation. Comparisons of the numerical results on wave diffraction forces and surface wave elevations at the cylinder to available analytical solutions demonstrate that excellent accuracy can be achieved by the SBFEM with a very small number of surface finite elements. The influence of varying the wave parameters as well as the system configuration on the system hydrodynamics, including the wave force, wave run-up, and diffracted wave contour is examined and extensive results on them are presented. This parametric study will help determine the various hydrodynamic effects of a concentric porous cylindrical structure.
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References
Chwang, A. T. (1983). “A porous wavemaker theory.” J. Fluid Mech., 132, 395–406.
Chwang, A. T., and Chan, A. T. (1998). “Interaction between porous media and wave motion.” Annu. Rev. Fluid Mech., 30, 53–84.
Chwang, A. T., and Dong, Z. (1985). “Wave-trapping due to a porous plate.” Proc., 15th Symp. on Naval Hydrodynamics, National Academy, Washington, D.C., 407–417.
Chwang, A. T., and Li, W. (1983). “A piston-type porous wavemaker theory.” J. Eng. Math., 17, 301–313.
Chwang, A. T., and Wu, J. (1994). “Wave scattering by submerged porous disk.” J. Eng. Mech., 120(12), 2575–2587.
Dalrymple, R. A., Losada, M. A., and Martin, P. A. (1991). “Reflection and transmission from porous structures under oblique wave attack.” J. Fluid Mech., 224, 625–644.
Darwiche, M. K. M., Williams, A. N., and Wang, K.-H. (1994). “Wave interaction with semiporous cylindrical breakwater.” J. Waterway, Port, Coastal, Ocean Eng., 120(4), 382–403.
Deeks, A. J., and Cheng, L. (2003). “Potential flow around obstacles using the scaled boundary finite-element method.” Int. J. Numer. Methods Fluids, 41(7), 721–741.
Faltas, M. S. (1996). “On oblique waves forcing by a porous cylindrical wall.” Int. J. Math. Math. Sci., 19(2), 351–362.
Fuchs, R. A. (1952). “On the theory of short-crested oscillatory waves.” Gravity Waves, National Bureau of Standards Circular No. 521, Dept. of Commerce, U.S. Government Printing Office, Washington, D.C., 187–200.
Fuhrman, D. R., and Madsen, P. A. (2006). “Short-crested waves in deep water: A numerical investigation of recent laboratory experiments.” J. Fluid Mech., 559, 391–411.
Guiney, D. C., Noye, B. J., and Tuck, E. O. (1972). “Transmission of water waves through small apertures.” J. Fluid Mech., 55, 149–161.
Huang, L. H., and Chao, H. I. (1992). “Reflection and transmission of water wave by porous breakwater.” J. Waterway, Port, Coastal, Ocean Eng., 118(5), 437–452.
Li, B., Cheng, L., and Deeks, A. J. (2004). “Wave diffraction by vertical cylinder using the scaled boundary finite element method.” Proc., WCCM VI and APCOM’04, Springer, Germany.
Li, Y., Sun, L., and Teng, B. (2003). “Wave action on double-cylinder structure with perforated outer wall.” Proc., 22nd Int. OMAE Conf. (CD-ROM), ASME, Cancun, Mexico, Paper No. OMAE2003-37094.
Madsen, O. S. (1974). “Wave transmission through porous structures.” J. Highw. Div., 100(3), 169–188.
Morse, P. M., and Feshbach, H. (1953). Methods of theoretical physics, McGraw-Hill, New York.
Nasser, M. S., and McCorquodale, J. A. (1974). “Experimental study of wave transmission.” J. Highw. Div., 100(4), 279–286.
Porter, D. (1972). “The transmission of surface waves through a gap in a vertical barrier.” Proc. Cambridge Philos. Soc., 71, 411–421.
Song, Ch., and Wolf, J. P. (1997). “The scaled boundary finite-element method—Alias consistent infinitesimal finite-element cell method—For elastodynamics.” Comput. Methods Appl. Mech. Eng., 147, 329–355.
Song, H., and Tao, L. (2008). “Scaled boundary FEM solution of wave diffraction by a square caisson.” Proc., 27th Int. OMAE Conf., ASME, Estoril, Portugal, Paper No. OMAE2007-57279.
Tao, L., Song, H., and Chakrabarti, S. K. (2007). “Scaled boundary FEM solution of short-crested wave diffraction by a vertical cylinder.” Comput. Methods Appl. Mech. Eng., 197, 232–242.
Taylor, G. (1956). “Fluid flow in regions bounded by porous surfaces.” Proc. R. Soc. London, Ser. A, 234(1199), 456–475.
Tsai, C. P., Jeng, D. S., and Hsu, J. R. C. (1994). “Computations of the almost highest short-crested waves in deep water.” Appl. Ocean. Res., 16(6), 317–326.
Tuck, E. O. (1971). “Transmission of water waves through small apertures.” J. Fluid Mech., 49, 65–74.
Vijayalakshmi, K., Neelamani, S., Sundaravadivelu, R., and Murali, K. (2007). “Wave runup on a concentric twin perforated circular cylinder.” Ocean Eng., 34(2), 327–336.
Wang, K.-H., and Ren, X. (1993). “Water waves on flexible and porous breakwater.” J. Eng. Mech., 119(5), 1025–1047.
Wang, K.-H., and Ren, X. (1994). “Wave interaction with a concentric porous cylinder system.” Ocean Eng., 21(4), 343–360.
Williams, A. N., and Li, W. (1998). “Wave interaction with a semi-porous cylindrical breakwater mounted on a storage tank.” Ocean Eng., 25(2–3), 195–219.
Wolf, J. P. (2003). The scaled boundary finite element method, Wiley, Chichester, England.
Yu, X., and Chwang, A. T. (1994a). “Wave-induced oscillation in harbor with porous breakwaters.” J. Waterway, Port, Coastal, Ocean Eng., 120(2), 125–144.
Yu, X., and Chwang, A. T. (1994b). “Wave motion through porous structures.” J. Eng. Mech., 120(5), 989–1008.
Yu, X., and Chwang, A. T. (1994c). “Water waves above submerged porous plate.” J. Eng. Mech., 120(6), 1270–1282.
Zhong, Z., and Wang, K. H. (2006). “Solitary wave interaction with a concentric porous cylinder system.” Ocean Eng., 33(7), 927–949.
Zhu, S. (1993). “Diffraction of short-crested waves around a circular cylinder.” Ocean Eng., 20(4), 389–407.
Zhu, S., and Moule, G. (1994). “Numerical calculation of forces induced by short-crested waves on a vertical cylinder of arbitrary cross-section.” Ocean Eng., 21(7), 645–662.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 135 • Issue 5 • September 2009
Pages: 200 - 212
Copyright
© 2009 ASCE.
History
Received: Jun 12, 2007
Accepted: Mar 13, 2009
Published online: Aug 14, 2009
Published in print: Sep 2009
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