A perturbation DRBEM model for weakly nonlinear wave run-ups around islands

Engineering Analysis with Boundary Elements

Volumn 33, Issue 1, 2009, Pages 63-76

  Zhu, Song Ping ^a   Liu, Huan Wen ^b   Marchant, Timothy R ^a  

^a UNIVERSITY OF WOLLONGONG   (Australia)

^b GUANGXI UNIVERSITY FOR NATIONALITIES   (China)

Author keywords

Nonlinear Boussinesq equations; The dual reciprocity boundary element method (DRBEM); Wave diffraction and refraction

Indexed keywords

BOUNDARY ELEMENT METHOD; CONTROL NONLINEARITIES; CONTROL THEORY; CYLINDERS (SHAPES); DIFFRACTION; DIFFRACTION GRATINGS; DISPERSION (WAVES); LINEAR EQUATIONS; NUMERICAL ANALYSIS; PERTURBATION TECHNIQUES; REFRACTION; WAVE EQUATIONS; WAVES;

BOUSSINESQ EQUATIONS; COLLOCATION POINTS; COMPUTATIONALLY EFFICIENT; CONICAL ISLANDS; DISPERSIVE EFFECTS; DOMAIN INTEGRALS; DUAL RECIPROCITY BOUNDARY ELEMENT METHODS; FIRST ORDERS; GOVERNING EQUATIONS; INCIDENT WAVES; LINEAR DIFFRACTION THEORIES; LONG WAVES; NEW MODELS; NON LINEARITIES; NONLINEAR BOUSSINESQ EQUATIONS; NONLINEAR CONTRIBUTIONS; NONLINEAR WAVES; NUMERICAL RESULTS; PARTIAL DERIVATIVES; PERTURBATION METHODS; THE DUAL RECIPROCITY BOUNDARY ELEMENT METHOD (DRBEM); VERTICAL CYLINDERS; WAVE DIFFRACTION AND REFRACTION; WAVE DIFFRACTIONS;

NONLINEAR EQUATIONS;

EID: 56249099339     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2008.03.009     Document Type: Article

References (60)

1. MacCamy RC, Fuchs RA. Wave forces on piles: a diffraction theory. US Army Corps of Engineering, Beach Erosion Board, Washington, DC, Technical Mem 69, 1954.
2. Homma S. On the behaviour of seismic sea waves around circular island. Geophys Mag 21 (1950) 199-208
3. Zhang Y.L., and Zhu S.-P. New solutions for the propagation of long water waves over variable depth. J Fluid Mech 278 (1994) 391-406
4. Zhu S.-P., and Zhang Y.L. Scattering of long waves around a circular Island mounted on a conical shoal. Wave Motion 23 (1995) 353-362
5. Liu H-W, Lin P-Z, Shankar NJ. An analytical solution of the mild-slope equation for waves around a circular island on a paraboloidal shoal. Coastal Eng 2004;51(5-6):421-37.
6. Lautenbacher C.C. Gravity wave refraction by islands. J Fluid Mech 41 (1970) 655-672
7. Liu PL-F, Cho Y-S, Fujima KJ. Numerical solutions of three-dimensional run-up on a circular island. In: International symposium: waves-physical and numerical modelling, University of British Columbia, Vancouver, Canada, 1994. p. 1031-40.
8. Liu P.L.-F., Cho Y.-S., Briggs M.J., Kanoglu U., and Synolakis C.E. Runup of solitary waves on a circular island. J Fluid Mech 302 (1995) 259-285
9. Chen HS, Mei CC. Oscillations and wave forces in a Man-made Harbor in the open sea. TR no. 190, Ralph M. Parsons Laboratory, Department of Civil Engineering, MIT, 1974.
10. Bettess P., and Zienkiewicz O.C. Diffraction and refraction of surface waves using finite and infinite elements. Int J Numer Methods Eng 2 (1977) 1271
11. Houston J.R. Combined refraction and diffraction of short waves using the finite element method. Appl Ocean Res 3 (1981) 163
12. Jonsson I.G., Skovgaard O., and Brink-Kjaer O. Diffraction and refraction calculations for waves incident on an island. J Mar Res 34 (1976) 469-496
13. Au M.C., and Brebbia C.A. Diffraction of water waves for vertical cylinders using boundary elements. Appl Math Modelling 7 (1983) 106-114
14. Zhu S.-P. A new DRBEM model for wave refraction and diffraction. Eng Anal Boundary Elements 12 (1993) 261-274
15. Zhu S.-P., Liu H.-W., and Chen K. A general DRBEM model for wave refraction and diffraction. Eng Anal Boundary Elements 24 (2000) 377-390
16. Liu H-W. Numerical modelling of the propagation of ocean waves. Doctoral dissertation. University of Wollongong, Wollongong, Australia, 2001.
17. Smith R., and Sprinks T. Scattering of surface waves by a conical island. J Fluid Mech 72 (1975) 373
18. Kanoglu U., and Synolakis C.E. Long wave runup on piecewise linear topographies. J Fluid Mech 374 (1998) 1-28
19. Peregrine D.H. Long waves on a beach. J Fluid Mech 27 (1967) 815-827
20. Abbott M.B., Petersen H.M., and Skovgaard O. On the numerical modelling of short waves in shallow water. J Hydraulic Res 16 (1978) 173-204
21. Rygg O. Nonlinear refraction-diffraction of surface waves in intermediate and shallow water. Coastal Eng 12 (1988) 191-211
22. Nwogu O. An alternative form of the Boussinesq equation for nearshore wave propagation. J Waterway Port Coastal Ocean Eng 119 (1993) 618-638
23. Wei G., and Kirby J.T. Time-dependent numerical code for extended Boussinesq equations. J Waterway Port Coastal Ocean Eng 121 (1995) 251-261
24. Wei G., Kirby J.T., Grilli S.T., and Subramanya R. A fully nonlinear Boussinesq model for surface waves, part 1: highly nonlinear unsteady waves. J Fluid Mech 294 (1995) 71-92
25. Chen Q., Kirby J.T., Dalrymple R.A., Kennedy A.B., and Chawla A. Boussinesq modeling of wave transformation, breaking and runup. J Waterway Port Coastal Ocean Eng 126 (2000) 48-56
26. Liu P.L.-F., Yoon S.B., and Kirby J.T. Nonlinear refraction-diffraction of waves in shallow water. J Fluid Mech 153 (1985) 185-201
27. Chen Y., and Liu P.L.-F. Modified Boussinesq equations and associated parabolic model for water wave propagation. J Fluid Mech 288 (1995) 351-381
28. Hwang L.-S., and Tuck E.O. On the oscillations of harbours of arbitrary shape. J Fluid Mech 42 (1970) 447-464
29. Nardini D., and Brebbia C.A. A new approach to free vibration analysis using boundary elements. In: Brebbia C.A. (Ed). Boundary element methods in engineering (1982), Springer, Berlin
30. Hsiao SS, Wu JH, Chiu YF. A perturbation-DRBEM model for wave refraction-diffraction. In: Seventh international offshore and polar engineering conference (ISOPE-97), Honolulu, USA, 1997. p. 308-12.
31. Hsiao SS, Weng WK, Chiu YF. Wave force on a circular island using perturbation-DRBEM. In: The eighth international offshore and polar engineering conference (ISOPE-98), vol. 1, Montreal, Canada, 1998. p. 231-6.
32. Rangogni R. A simple procedure to solve the mild-slope equation using BEM and perturbation expansion technique-part 1. In: Brebbia C.A. (Ed). Boundary elements X vol. 1 (1988), Computational Mechanics Publications, Springer, Southampton, Berlin 331-343
33. Kriebel D.L. Nonlinear wave interaction with a vertical circular cylinder part, I: diffraction theory. Ocean Eng 17 (1990) 345-377
34. Kriebel D.L. Nonlinear wave interaction with a vertical circular cylinder, part II: wave runup. Ocean Eng 19 (1992) 75-99
35. Mei C.C. The applied dynamics of ocean surface waves (1989), World Scientific, Singapore
36. Sommerfeld A. Partial differential equations in physics (1949), Academic Press, New York
37. Givoli D. Non-reflecting boundary conditions. J Comput Phys 94 (1991) 1-29
38. Engquist E., and Majda A. Absorbing boundary conditions for the numerical simulation of waves. Math Comput 31 (1977) 629-651
39. Molin B. Second order diffraction loads upon three-dimensional bodies. Appl Ocean Res 1 (1979) 197-202
40. Newman J.N. The second-order wave force on a vertical cylinder. J Fluid Mech 320 (1996) 417-443
41. Nardini D., and Brebbia C.A. Transient boundary element elastidynamics using the dual reciprocity method and model superposition. Boundary element VIII vol. 1 (1986), Computational Mechanics Publications, Springer, Southampton, Berlin
42. Partridge P.W., and Wrobel L.C. The dual reciprocity method for spontaneous ignition. Int J Numer Methods Eng 30 (1990) 953-963
43. Zhu S.-P., and Zhang Y.L. Improvement on dual reciprocity boundary element method for equations with convective terms. Commun Numer Methods Eng 10 (1994) 361-371
44. Zhang Y.L., and Zhu S.-P. On the choice of interpolation functions used in the dual-reciprocity boundary-element method. Eng Anal Boundary Elements 13 (1994) 387-396
45. Partridge P.W., and Brebbia C.A. Computer implementation of the BEM dual reciprocity method for the solution of Poisson type equations. Software Eng Workstations 5 (1989) 199-206
46. Lu X-P. On the application of the thin plate spline in the LTDRM for solving linear and nonlinear diffusion problems. In: Proceedings of the second biennial Australian engineering mathematics conference, Sydney, Australia, 1996. p. 437-43.
47. Zhu S.-P., Liu H.-W., and Lu X.-P. A combination of the LTDRM and the ATPS in solving diffusion problems. Eng Anal Boundary Elements 21 3 (1998) 285-289
48. Zhu S.-P., and Liu H.-W. On the application of the generalized multiquadric bases in conjunction with the LTDRM to solve transient nonlinear diffusion equations. Appl Math Comput 96 (1998) 161-175
49. Chen J.T., Chang M.H., Chen K.H., and Lin S.R. The boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function. J Sound Vib 257 4 (2002) 667-711
50. Chen J.T., Chen I.L., Chen K.H., Yeh Y.T., and Lee Y.T. A meshless method for free vibration of arbitrarily shaped plates with clamped boundaries using radial basis function. Eng Anal Boundary Elements 28 5 (2004) 535-545
51. Reutskiy S.Y., and Chen C.S. Approximation of multivariate functions and evaluation of particular solutions using Chebyshev polynomial and trigonometric basis functions. Int J Numer Methods Eng 67 (2006) 1811-1829
52. Hsiao S-S, Chang J-R, Chang C-M. Improving the accuracy of DRBEM wave model by using radial basis function. In: Proceedings of the seventeenth international offshore and polar engineering conference, Lisbon, Portugal, 2007. p. 2296-301.
53. Micchelli C.A. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constr Approx 2 (1986) 11-22
54. Zhu S.-P. Particular solutions associated with the Helmholtz operator used in DRBEM. Boundary Elements Abstr 4 (1993) 231-233
55. Fairweather G., and Karageorghis A. The method of fundamental solutions for elliptic boundary value problems. Adv Comput Math 9 (1998) 69-95
56. Li J., Hon Y.C., and Chen C.-S. Numerical comparisons of two meshless methods using radial basis functions. Eng Anal Boundary Elements 26 3 (2002) 205-225
57. Lin M.C., and Hsiao S.S. Experimental study on wave-current interactions around a large scale cylinder. Coastal Eng Jpn 38 1 (1995) 39-61
58. Hsiao SS, Weng WK, Lin MC. Wave pressure on a large cylinder in a wave-current coexisting field. In: The ninth international offshore and polar engineering conference, Brest, France, 1999. p. 441-5.
59. Provis DG. Propagation of water waves near an island. PhD thesis, University of Essex, 1975.
60. Sprinks T., and Smith R. Scale effects in a wave-refraction experiment. J Fluid Mech 129 (1983) 455-471