Second-Order Radiation Boundary Condition for Water Wave Simulation with Large Angle Incidence
Publication: Journal of Engineering Mechanics
Volume 129, Issue 12
Abstract
A finite-element method (FEM) is used to simulate water wave propagation with large angle incidence at exterior boundaries. In this paper, the radiation boundary condition is expanded to a second-order approximation and a quadratic shape function is used in the FEM wave model. Cases used for verifications include wave scattering around a vertical cylinder and wave propagation over a submerged circular shoal with concentric contours. Numerical calculations based on this second-order radiation boundary condition are found to be in good agreement with theoretical and experimental results available. The numerical predictions show that this model has made a very good improvement over the first-order radiation boundary conditions for oblique wave incidence in coastal engineering.
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References
Becker, E. B., Carey, G. F., and Oden, J. T. (1981). Finite elements: An introduction, Prentice-Hall, Englewood Cliffs, N.J.
Behrendt, L. (1985). “A finite element model for water wave diffraction including boundary absorption and bottom friction.” Series Paper 37, Institute of Hydrodynamics and Hydraulic Engineering, Univ. of Denmark, Lyngby, Denmark.
Berkhoff, J. C. W. (1972). “Computation of combined refraction-diffraction.” Proc., 13th Int. Conf. on Coastal Engineering, ASCE, New York, 471–490.
Bettess, P., and Zienkiewicz, O. C.(1977). “Diffraction and refraction of surface waves using finite and infinite element.” Int. J. Numer. Methods Eng., 11(8), 1271–1290.
Booij, N. (1981). “Gravity waves on water with non-uniform depth and current.” Rep. No. 81-1, Dept. of Civil Engineering, Delft Univ. of Technology, The Netherlands.
Chen, B. S., and Tsay, T. K. (1990). “Application of local radiation condition to water-wave numerical modeling.” Proc., 12th Conf. on Ocean Engineering in ROC, Taichung, Taiwan, 1–9 (in Chinese).
Chen, H. S., and Mei, C. C. (1974). “Oscillation and wave force on an offshore harbor.” Rep. No. 190, Ralph M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, Mass.
Dalrymple, R. A., and Kirby, J. T.(1988). “Models for very wide-angle water waves and wave diffraction.” J. Fluid Mech., 192, 33–50.
Dalrymple, R. A., Suh, K. D., Kirby, J. T., and Chag, J. W.(1989). “Models for very wide-angle water waves and wave diffraction. Part 2: irregular bathymetry.” J. Fluid Mech., 201, 299–322.
Dingemans, M. W. (1983). “Verification of numerical wave propagation method with field measurements: CREDIZ verification Haringvliet.” Rep W488, Pt. 1, Delft Hydraulic Laboratory, Delft, The Netherlands.
Givoli, D.(1991). “Non-reflecting boundary conditions.” J. Comput. Phys., 94(1), 1–29.
Givoli, D., and Keller, J. B.(1994). “Special finite elements for use with high-order boundary conditions.” Comput. Methods Appl. Mech. Eng., 119(3–4), 199–213.
Hagstrom, T.(1999). “Radiation boundary conditions for the numerical simulation of waves.” Acta Numerica, 8, 47–106.
Hsu, T. W., Tsay, T. K., Yan, C. C., and Chen, B. S. (1998). “Simulations on wave field in nearshore zone by finite element method.” Proc., 20th Ocean Engineering Conf. in ROC, Keelung, Taiwan, 491–499 (in Chinese).
Ito, Y., and Tanimoto, K. (1972). “A method of numerical analysis of wave propagation application to wave diffraction and refraction.” Proc., 13th Int. Conf. on Coastal Engineering, ASCE, New York, 503–522.
Kirby, J. T.(1986). “Rational approximations in the parabolic equation method for water waves.” Coastal Eng., 10(6), 503–522.
MacCamy, R. C., and Fuchs, R. A. (1954). “Wave force on piles: a diffraction theory.” Institute of Engineering Research, Waves Investigation Laboratory, Series 3, Issue 334, Berkeley, Calif.
Panchang, V., Chen, W., Xu, B., Schlenker, K., Demirbilek, Z., and Okihiro, M.(2000). “Exterior bathymetric effects in elliptic harbor wave models.” J. Waterw., Port, Coastal, Ocean Eng., 126(2), 71–78.
Radder, A. C.(1979). “On the parabolic equation method for water wave propagation.” J. Fluid Mech., 95, 159–176.
Tsay, T. K., and Liu, P. L.-F.(1983). “A finite element model for wave refraction and diffraction.” Appl. Ocean. Res., 5(1), 30–37.
Tsynkov, S. V.(1998). “Numerical solution of problems on unbounded domains.” Appl. Numer. Math., 27(4), 465–532.
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Copyright © 2003 American Society of Civil Engineers.
History
Received: Oct 1, 2001
Accepted: May 14, 2003
Published online: Nov 14, 2003
Published in print: Dec 2003
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