Dual Boundary Element Analysis of Normal Incident Wave Passing a Thin Submerged Breakwater with Rigid, Absorbing, and Permeable Boundaries
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 130, Issue 4
Abstract
In this paper, the dual integral formulation is derived for solving the scattering problem of normal incident wave passing a thin vertical and inclined barrier with rigid boundary condition which is descending from the water surface to a depth. Absorbing and porous boundary conditions are both considered. The breakwater thickness is assumed to be zero since it is negligible in comparison with the water depth and the wavelength of the incident wave. Although the multidomain boundary element method (BEM) can solve boundary value problems with degenerate boundaries by dividing the interesting domain into two subdomains, the hypersingular formulation provides the key to solve the problem more efficiently in a single domain. To demonstrate the effects of the breakwater with rigid, absorbing, and porous boundary conditions for the energy dissipation by the barrier, the transmission and reflection coefficients of the scattering problem are determined by the developed dual BEM program. In addition, the results are obtained for the cases of wave scattering by the barrier with zero thickness in constant water depth and are compared with the analytical solutions, the multidomain BEM solution, and the experimental data.
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References
Aliabadi, M. H.(1997). “Boundary element formulations in fracture mechanics.” Appl. Mech. Rev., 50, 83–96.
Aliabadi, M. H., and Saleh, A. L.(2002). “Fracture mechanics analysis of cracking in plain and reinforced concrete using the boundary element method.” Eng. Fract. Mech., 69(2), 267–280.
Blandford, G. E., Ingraffea, A. R., and Liggett, J. A.(1981). “Two-dimensional stress intensity factor computations Using the Boundary Element Method.” Int. J. Numer. Methods Eng., 17, 387–404.
Chen, K. H., Chen, J. T., Chou, C. R., and Yueh, C. Y.(2002). “Dual boundary element analysis of oblique incident wave passing a thin submerged breakwater.” Eng. Anal. Bound. Elem., 26(10), 917–928.
Chen, J. T., and Hong, H.-K.(1993). “On the dual integral representation of boundary value problem in Laplace equation.” Bound. Elem. Abstracts, 3, 114–116.
Chen, J. T., and Chen, K. H.(1998). “Dual integral formulation for determining the acoustic modes of a two-dimensional cavity with a degenerate boundary.” Eng. Anal. Bound. Elem., 21, 105–116.
Chen, J. T., and Hong, H.-K.(1999). “Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series.” Appl. Mech. Rev., 52(1), 17–33.
Chen, J. T., Lin, S. R., Chen, K. H., Chen, I. L., and Chyuan, S. W.(2003). “Eigenanalysis for membranes with stringers using conventional BEM in conjunction with SVD technique.” Comput. Methods Appl. Mech. Eng., 192, 1299–1322.
Dean, R. G., and Dalrymple, R. A. (1984). Water wave mechanics for enginers and scientists, Prentice-Hall, Englewood Cliffs, N.J.
Hong, H.-K., and Chen, J. T.(1988). “Derivations of integral equations of elasticity.” J. Eng. Mech., 114(6), 1028–1044.
Hsu, H. H., and Wu, Y. C.(1999). “Scattering of water wave by a submerged horizontal plate and a submerged permeable breakwater.” Ocean Eng., 26, 325–341.
Jones, D. B., Lee, J.-J., and Raichlen, F. (1979). “A transportable breakwater for nearshore application.” Proc., Specialty Conf. Civil Engineering in Ocean IV, Vol. 1, 433–456.
Lafe, O. E., Montes, J. S., Cheng, A. H. D., Liggett, J. A., and Liu, L.-F.(1980). “Singularities in Darcy flow through porous media.” J. Hydraul. Div., Am. Soc. Civ. Eng., 106(6), 977–997.
Lee, M. M., and Chwang, A. T.(2000). “Scattering and radiation of water by permeable barriers.” Phys. Fluids, 12, 54–65.
Linton, C. M., and McIver, P.(2000). “Green’s functions for water waves in porous structures.” Appl. Ocean. Res., 22, 1–12.
Liu, P. L. F., and Abbaspour, M.(1982). “Wave scattering by a rigid thin barrier.” Proc. Am. Soc. Civ. Eng., 108, 479–491.
Losada, I. J., Losada, M. A., and Roldan, J.(1992). “Propagation of oblique incident waves past rigid vertical thin barriers.” Appl. Ocean. Res., 14, 191–199.
Losada, I. J., Patterson, M. D., and Losada, M. A.(1997). “Harmonic generation past a submerged porous step.” Coastal Eng., 31, 281–304.
McIver, P.(1999). “Water-wave diffraction by thin porous breakwater.” J. Waterw., Port. Coastal, Ocean Eng., 125(2), 66–70.
Raichlen, F., and Lee, J.-J. (1978). “An inclined plat wave generator.” Proc., 16th Coastal Engineering Conf., 388–399.
Sommerfeld, A. (1964). “Lectures on theoretical physics.” Partial differential equations in physics, Vol. VI, Chap. 28, Academic, New York.
Tsaur, D. H., Yueh, C. Y., Chang, K. H., and Yang, Y. C. (2000). “A study on wave scattering by submerged plate-type breakwater with absorbing boundary.” Proc., 12th Hydraulic Engineering Conf., Taiwan, R.O.C., 168–174 (in Chinese).
Ursell, F.(1974). “The effect of a fixed vertical barrieron surface waves in deep water.” Proc. Cambridge Philos. Soc., 43(3), 374–382.
Wiegel, R. L.(1960). “Transmission of wave past a rigid vertical thin barrier.” J. Waterw. Harbors Div., Am. Soc. Civ. Eng., 86, 1–12.
Wu, Y. C., Hsu, R. C., and Chen, J. C. (1999). “The interaction of oblique wave with submerged porous breakwaters.” Proc., 21th Ocean Engineering Conf., Taiwan, R.O.C., 259–266 (in Chinese).
Yip, T. L., and Chwang, T.(1998). “Water wave control by submerged pitching porous plate.” J. Eng. Mech., 124(4), 428–434.
Yu, X.(1995). “Diffraction of water waves by porous breakwaters.” J. Waterw., Port. Coastal, Ocean Eng., 121(6), 275–282.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 130 • Issue 4 • July 2004
Pages: 179 - 190
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Dec 11, 2002
Accepted: Nov 21, 2003
Published online: Jun 15, 2004
Published in print: Jul 2004
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