Meshless numerical simulation for fully nonlinear water waves

International Journal for Numerical Methods in Fluids

Volumn 50, Issue 2, 2006, Pages 219-234

  Wu, Nan Jing ^a   Tsay, Ting Kuei ^a   Young, D L ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Meshless numerical method; Method of fundamental solutions; Moving boundary; Nonlinear water waves; Radial basis functions

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; NUMERICAL METHODS;

MESHLESS NUMERICAL METHOD; METHOD OF FUNDAMENTAL SOLUTIONS; NONLINEAR WATER WAVES;

WATER WAVES;

FLUID MECHANICS; MATHEMATICAL ANALYSIS; WATER; WAVE;

EID: 29544448768     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.1051     Document Type: Article

References (30)

1. Peregrine DH. Long waves on beach. Journal of Fluid Mechanics 1967; 27:815-827.
2. Issacson M, Cheung KF. Second order wave diffraction around two-dimensional bodies by time domain method. Applied Ocean Research 1991; 13:175-186.
3. Nwogu O. An alternative form of Boussinesq equations for near shore wave propagation. Journal of Waterway, Port, Coastal, and Ocean Engineering (ASCE) 1993; 119:618-638.
4. Massel SR. Harmonic generation by waves propagating over a submerged step. Coastal Engineering 1983; 7:357-380.
5. Vada T. A numerical solution of the second-order wave-diffraction problem for a submerged cylinder of arbitrary shape. Journal of Fluid Mechanics 1987; 174:23-37.
6. Palm E. Nonlinear wave reflection from a submerged circular cylinder. Journal of Fluid Mechanics 1991; 233:49-63.
7. Sulisz W. Diffraction of second-order surface waves by semisubmerged horizontal rectangular cylinder. Journal of Waterway, Port, Coastal, and Ocean Engineering (ASCE) 1993; 119:160-171.
8. Glauss G. Dramas of the sea: episodic waves and their impact on offshore structures. Applied Ocean Research 2002; 24:147-151.
9. Lo DC, Young DL. Arbitrary Lagrangian-Eulerian finite element analysis of free surface flow using a velocity-vorticity formulation. Journal of Computational Physics 2004; 195:175-201.
10. Longuet-Higgins HS, Cokelet ED. The deformation of steep waves on water. I. A numerical method of computation. Proceedings of the Royal Society of London 1976; A350:1-26.
11. Issacson M. Nonlinear wave effects on fixed and floating bodies. Journal of Fluid Mechanics 1982; 120: 267-281.
12. Dommermuth DG, Yue DKP. Numerical simulations of nonlinear axisymmetric flows with a free surface. Journal of Fluid Mechanics 1987; 178:195-219.
13. Grilli ST, Skourup J, Svendsen IA. An efficient boundary element method for nonlinear water waves. Engineering Analysis with Boundary Elements 1989; 6:97-107.
14. Cooker MJ, Peregrine DH, Skovggard O. The interaction between a solitary wave and a submerged semicircular cylinder. Journal of Fluid Mechanics 1990; 215:1-22.
15. Ohyama T, Nadaoka K. Development of a numerical wave tank for analysis of nonlinear and irregular wave field. Fluid Dynamics Research 1991; 8:231-251.
16. Grilli ST, Guyenne P, Dias F. A fully nonlinear model for three-dimensional overturning waves over an arbitrary bottom. International Journal for Numerical Methods in Fluids 2001; 35:829-867.
17. Tsai WT, Yue DKP. Computation of nonlinear free-surface flows. Annual Review of Fluid Mechanics 1996; 28:249-278.
18. Rokhlin V. Rapid solution of integral equations of classical potential theory. Journal of Computational Physics 1985; 60:187-207.
19. Hackbusch W, Nowak ZP. On the fast matrix multiplication in the boundary element method by panel clustering. Numerische Mathematik 1989; 54:463-491.
20. Beylkin G, Coifman R, Rokhlin V. Fast wavelet transforms and numerical algorithms I. Communications on Pure and Applied Mathematics 1991; 44:141-183.
21. Hardy RL. Multiquadric equations of topography and other irregular surfaces. Journal of Geophysical Research 1971; 76:1905-1915.
22. Franke C. Scattered data interpolation: test of some methods. Mathematics of Computation 1982; 38:181-200.
23. Moody J, Darken C. Fast-learning in networks of local tuned processing units. Neural Computation 1989; 1:281-294.
24. Kansa JE. Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics - II. Solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers and Mathematics with Applications 1990; 19:127-145.
25. Wong SM, Hon YC, Golberg MA. Compactly supported radial basis functions for shallow water equations. Applied Mathematics and Computation 2002; 127:79-101.
26. Golberg MA, Chen CS. The Method of Fundamental Solutions for Potential, Helmholtz and Diffusion Problems, in Boundary Integral Methods - Numerical and Mathematical Aspects. Computational Mechanics Publications: Southampton, Boston, 1998; 103-176.
27. Ursell F, Dean RG, Yu YS. Forced small amplitude water waves: a comparison of theory and experiment. Journal of Fluid Mechanics 1960; 7:32-53.
28. Luth HR, Klopman G, Kitou N. Kinematics of waves breaking partially on an offshore bar; LDV measurements of waves with and without a net onshore current. Technical Report H-1573, Delft Hydraulics, Delft, The Netherlands, 1994.
29. Gobbi MF, Kirby JT. Wave evolution over submerged sills: tests of a high order Boussinesq model. Coastal Engineering 1999; 37:57-96.
30. Li B, Fleming CA. Three-dimensional model of Navier-Stokes equations. Journal of Waterway, Port, Coastal, and Ocean Engineering (ASCE) 2001; 127:16-25.