Simulation Of Directional Waves In A Numerical Basin By A Desingularized Integral Equation Approach

Ocean Engineering 27 (2000) 603–624
www.elsevier.com/locate/oceaneng

Simulation of directional waves in a numerical
basin by a desingularized integral equation
approach
A.N. Williams*, W.W. Crull
Department of Civil and Environmental Engineering, University of Houston, Houston, TX 77204-4791,
USA
Received 5 October 1998; accepted 6 January 1999

Abstract
A numerical solution is developed to investigate the generation and propagation of smallamplitude water waves in a semi-infinite rectangular wave basin. The three-dimensional wave
field is produced by the prescribed “snake-like” motion of an array of segmented wave generators located along the wall at one end of the tank. The solution technique is based on the
boundary element approach and uses an appropriate three-dimensional Green function which
explicitly satisfies the tank-wall boundary conditions. The Green function and its derivatives
which appear in the integral equation formulation can be shown to be slowly convergent when
the source and field points are in close proximity. Therefore, when computing the velocity
potentials on the wave generators, the source points are chosen outside the fluid domain,
thereby ensuring the rapid convergence of these functions and rendering the integral equations
non-singular. Numerical results are shown which illustrate the influence of the various wavemaker and basin parameters on the generated wave field. Finally, the complete wave field
produced by the diffraction of oblique waves by a vertical circular cylinder in a basin is
presented.  1999 Elsevier Science Ltd. All rights reserved.
Keywords: Directional waves; Laboratory waves; Wave diffraction; Wave basin; Wave generation

* Corresponding author. Tel.: ϩ 1-713-743-4269; fax: ϩ 1-713-743-4260; e-mail: anwilliams@
jetson.uh.edu
0029-8018/00/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved.
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