Hostname: page-component-7dd5485656-g8tfn Total loading time: 0 Render date: 2025-10-31T05:25:09.868Z Has data issue: false hasContentIssue false
  • English
  • Français

The Method of Fundamental Solutions for Water-Wave Diffraction by Thin Porous Breakwater

Published online by Cambridge University Press:  31 March 2011

C. H. Tsai  and
D. L. Young
C. H. Tsai
Affiliation:
Department of Civil Engineering & Hydrotech Research Institute, National Taiwan University Taipei, Taiwan 10617, R.O.C.
D. L. Young*
Affiliation:
Department of Civil Engineering & Hydrotech Research Institute, National Taiwan University Taipei, Taiwan 10617, R.O.C.
*
**Professor, corresponding author
Get access

Abstract

The method of fundamental solutions (MFS) and domain decomposition method (DDM) are employed to solve the water-wave diffraction by a thin porous vertical breakwater of semi-infinite extent. Based on the linearized theory of water waves, the problem can be reduced to a boundary value problem with degenerate boundary. In contrast to other mesh dependent numerical method, the MFS is easier and more efficient to handle degenerate boundary value problems. Various incident wave angles and porous parameters are included to validate the power of the proposed numerical scheme. The present results demonstrate the MFS is sufficiently accurate and feasible to be used to predict water-wave diffraction by a thin permeable breakwater by comparing with literature.

Keywords

Method of fundamental solutionsDomain decomposition methodPorous breakwaterWater-wave diffractionDegenerate boundary

Information

Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 1 , March 2011 , pp. 149 - 155
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

1.Kupradze, V. D. and Aleksidze, M. A., “The Method of Functional Equations for the Approximate Solution of Certain Boundary Value Problem,” USSR Computational Mathematics and Mathematical Physics, 4, pp. 82–126 (1964).CrossRefGoogle Scholar
2.Johnston, R. L. and Fairweather, G., “The Method of Fundamental Solutions for Problems in Potential Flow,” Applied Mathematical Modelling, 8, pp. 265–270 (1984).Google Scholar
3.Karageorghis, A. and Fairweather, G., “The Method of Fundamental Solutions for the Solution of Nonlinear Plane Potential Problems,” IMA Journal of Numerical Analysis, 9, pp. 231–242 (1989).CrossRefGoogle Scholar
4.Karageorghis, A. and Fairweather, G., “The Almansi Method of Fundamental Solutions for Solving Biharmonic Problems,” International Journal for Numerical Methods in Engineering, 26, pp. 1665–1682 (1988).Google Scholar
5.Karageorghis, A. and Fairweather, G., “The Simple Layer Potential Method for Fundamental Solutions for Certain Biharmonic Problems,” International Journal for Numerical Methods Fluids, 9, pp. 1221–1234 (1989).CrossRefGoogle Scholar
6.Golberg, M. A., “The Method of Fundamental Solutions for Poisson's Equation,” Engineering Analysis with Boundary Elements, 16, pp. 205–213 (1995).Google Scholar
7.Chen, C. W., Fan, C. M., Young, D. L., Murugesan, K. and Tsai, C. C., “Eigenanalysis for Membranes with Stringers Using the Methods of Fundamental Solutions and Domain Decomposition,” CMES-Computer Modeling in Engineering and Sciences, 8, pp. 29–44 (2005).Google Scholar
8.Young, D. L., Fan, C. M., Tsai, C. C. and Chen, C. W., “The Method of Fundamental Solutions and Domain Decomposition Method for Degenerate Seepage Flow Net Problems,” Journal of the Chinese Institute of Chemical Engineers, 29, pp. 63–73 (2006).CrossRefGoogle Scholar
9.Havelock, T. H., “The Pressure of Water Waves upon a Fixed Obstacle,” Proceedings of the Royal Society of London. Series A, England, 175, pp. 409–421 (1940).Google Scholar
10.Yu, X., “Diffraction of Water Waves by Porous Breakwaters,” Journal of Waterway, Port, Coastal, and Ocean Engineering, 121, pp. 275–282 (1995).Google Scholar
11.McIver, P., “Water-wave Diffraction by Thin Porous Breakwater,” Journal of Waterway, Port, Coastal, and Ocean Engineering, 125, pp. 66–70 (1999).Google Scholar
12.McIver, P., “Diffraction of Water Waves by a Segmented Permeable Breakwater,” Journal of Waterway, Port, Coastal, and Ocean Engineering, 131, pp. 69–76 (2005).Google Scholar
13.Chen, K. H., Chen, J. T., Lin, S. Y. and Lee, Y. T., “Dual Boundary Element Analysis of Normal Incident Wave Passing a Thin Submerged Breakwater with Rigid, Absorbing, and Permeable Boundaries,” Journal of Waterway, Port, Coastal, and Ocean Engineering, 130, pp. 179–190 (2004).Google Scholar
14.Chan, T. F., Glowinski, R., Periaux, J. and Widlund, O. B., Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia (1989).Google Scholar
15.Chan, T.F., Glowinski, R., Periaux, J. and Widlund, O.B., Domain Decomposition Methods, SIAM, Philadelphia (1990).Google Scholar
16.Ramachandran, P. A., “Method of Fundamental Solutions: Singular Value Decomposition Analysis,” Communications in Numerical Methods in Engineering, 18, pp. 789–801 (2002).Google Scholar
17.Penney, W. G. and Price, A. T., “The Diffraction Theory of Sea Waves and the Shelter Afforded by Breakwaters,” Philosophical Transactions of the Royal Society of London, Series A, England, 244, pp. 236–253 (1952).Google Scholar