General DRBEM model for wave refraction and diffraction

Engineering Analysis with Boundary Elements

Volumn 24, Issue 5, 2000, Pages 377-390

  Zhu, Song Ping ^a   Liu, Huan Wen ^a,c   Chen, Ke ^b  

^a UNIVERSITY OF WOLLONGONG   (Australia)

^b UNIVERSITY OF LIVERPOOL   (United Kingdom)

^c GUANGXI UNIVERSITY FOR NATIONALITIES   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; COMPUTATIONAL FLUID DYNAMICS; DIFFRACTION; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; REFRACTION; SURFACE WAVES;

DUAL RECIPROCITY BOUNDARY ELEMENT METHODS (DRBEM); MILD-SLOPE EQUATIONS;

TSUNAMIS;

EID: 0034178972     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0955-7997(00)00015-1     Document Type: Article

References (44)

1. González FI, Tsunamii. Scientific American, May, 1999.
2. Bettess P, Zienkiewicz OC. Diffraction and refraction of surface waves using finite and infinite elements. Int J Numer Meth Engng 1977;2:1271.
3. Peregrine DH. Long waves on a beach. J Fluid Mech 1967;27:815-27.
4. Zhang YL, Zhu S-P. New solutions for the propagation of long water waves over variable depth. J Fluid Mech 1994;278:391-406.
5. Homma S. On the behaviour of seismic sea waves around circular island. Geophys Mag 1950;21:199-208.
6. Houston JR. Combined refraction and diffraction of short waves using the finite element method. Appl Ocean Res 1981;3:163.
7. Tsay T-K, Liu PL-F. A finite element model for wave refraction and diffraction. Appl Ocean Res 1983;5:30-7.
8. Li B, Anastasiou K. Efficient elliptic solvers for the mild-slope equation using the multigrid technique refraction-diffraction. Coastal Engng 1992;16:245-66.
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. Berkhoff JCW. Computation of combined refraction-diffraction. 13th International Conference on Coastal Engineering, Vancouver, 1972. p. 471-90.
11. Smith R, Sprinks T. Scattering of surface waves by a conical island. J Fluid Mech 1975;72:373.
12. Mei CC. The applied dynamics of ocean surface waves. Singapore: World Scientific, 1989 (p. 62-6).
13. Booij N. Gravity waves on water with non-uniform depth and current. Doctoral thesis, Technical University of Delft, The Netherlands, 1981.
14. Booij N. A note on the accuracy of the mild-slope equation. Coastal Engng 1983;7:191-203.
15. Massel SA. Extension of mild-slope model for surface waves. Coastal Engng 1993;19:97-126.
16. MacCamy RC, Fuchs RA. Wave forces on piles: a diffraction theory. US Army Corps of Engineering, Beach Erosion Board, Washington, DC, Tech Mem 69, 1954.
17. Houston JR. Modeling of short wave using the finite element method. Proceedings of the Third International Conference on Finite Elements in Water Resources, 1980. p. 5.181-95.
18. Zhu S-P. A new DRBEM model for wave refraction and diffraction. Engng Anal Boundary Elements 1993;12:261-74.
19. Zhu S-P, Zhang YL. Combined refraction and diffraction of short waves using the dual-reciprocity boundary-element method. Appl Ocean Res 1995;17:315-22.
20. Berkhoff JCW. Mathematical models for simple harmonic linear water waves, wave diffraction and refraction. Delft Hydraulic Laboratory, Pub. No. 163, 1976.
21. Sommerfeld A. Partial differential equations in physics, Lectures on theoretical physics, vol. 6. New York: Academic Press, 1964 (335pp.).
22. Nardini D, Brebbia CA. A new approach to free vibration analysis using boundary elements. In: Brebbia CA, editor. Boundary element methods in engineering, Berlin: Springer, 1982.
23. Nardini D, Brebbia CA. Transient boundary element elastidynamics using the dual reciprocity method and model superposition, Boundary element VIII, vol. 1. Berlin: Springer, 1986 (Southampton: Computational Mechanics Publications).
24. Partridge PW, Brebbia CA. Computer implementation of the BEM dual reciprocity method for the solution of Poisson type equations. Software Engng Workstations 1989;5:199-206.
25. Partridge PW, Wrobel LC. The dual reciprocity method for spontaneous ignition. Int J Num Meth Engng 1990;30:953-63.
26. Zhu S-P, Zhang YL. Improvement on dual reciprocity boundary element method for equations with convective terms. Commun Num Meth Engng 1994;10:361-71.
27. Zhang YL, Zhu S-P. On the choice of interpolation functions used in the dual-reciprocity boundary-element method. Engng Anal Boundary Elements 1994;13:387-96.
28. Duchon J. Spline minimizing rotation-invariant seminorms in Sobolev space. Constructive theory of functions of several variables, Lecture Notes in Mathematics, vol. 571. Berlin: Springer, 1977.
29. Golberg MA. The method of fundamental solutions for Poisson's equation. Betech IX, Southampton: Computational Mechanics Publications, 1994.
30. Bridges TR, Wrobel LC. A dual reciprocity formulation for elasticity problems with body forces using augmented thin plate splines. Commun Num Meth Engng 1996;12:209-20.
31. Zhu S-P, Liu H-W, Lu X-P. A combination of the LTDRM and the ATPS in solving linear diffusion problems. Engng Anal Boundary Elements 1998;21:285-9.
32. Madych WR, Nelson SA. Multivariate interpolation and conditionally positive definite functions II. Math Comp 1990;54:211-30.
33. Powell MJD. The uniform convergence of thin plate splines in two dimensions. In: Univ. of Cambridge Numer. Annual Report DAMTP 1993/NA 16.
34. Wu Z, Shaback R. Local error estimates for radial basis function interpolation of scattered data. EMA J Num Anal 1993;13:13-27.
35. Golberg MA, Chen CS, Karur S. Improved multiquadric approximation for partial differential equations. Engng Anal Boundary Elements 1996;18:9-17.
36. Zhu S-P, Liu H-W. On the application of the multiquadric bases in conjunction with the LTDRM method to solve nonlinear diffusion equations. Appl Math Comput 1998;96:161-75.
37. Micchelli CA. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Construct Approx 1986;2:11-22.
38. Zhu S-P. Particular solutions associated with the Helmholtz operator used in DRBEM. Boundary Elements Abs 1993;4:231-3.
39. Vastano AC, Reid RO. Tsunami response for islands: verification of a numerical procedure, . J. Mar Res 1967;25:129-39.
40. Jonsson IG, Skovgaard O, Brink-Kjaer O. Diffraction and refraction calculations for waves incident on an island. J Mar Res 1976;34:469-96.
41. Lautenbacher CC. Gravity wave refraction by islands. J Fluid Mech 1970;41:655-72.
42. Golberg MA. Solution methods for integral equations: theory and applications. New York: Plenum Press, 1978.
43. Power H, Wrobel, LC. Boundary integral methods in fluid mechanics. Southampton, UK: Computational Mechanics Publications, 1995.
44. Poulin S. A boundary element model for diffraction of water waves on varying water depth. Doctoral thesis, Technical University of Denmark, 1997.