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http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53587#.VMnhhyzQrzE
Author(s)
Mingdong Lv1, Hui Li1, Huilong Ren1, Xiaobo Chen2
Affiliation(s)
1College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China.
2Bureau Veritas Research Department, Singapore City, Singapore.
ABSTRACT
We consider a vertical circular cylinder on which the vertical variation of water diffraction waves is to be represented by a series of Laguerre functions using Laguerre Polynomials . The variation is assumed to be of the form with the integer n depending on the radius of cylinder. Generally, the integer n increases for a cylinder of larger diameter. The usual approximation by Laguerre functions is extended by introducing a scale parameter. The convergence of Laguerre series is then dependent on the value of the scale parameter s. The analytical and numerical computations of series coefficients are performed to study the number of series terms to keep the same accuracy. Indeed, the choice of integer n depends on the scale parameter. Furthermore, diffraction waves generated by a semi-sphere inside the cylinder are evaluated on the cylinder surface. It is shown that the approximation by Laguerre series for diffraction waves on the cylinder is effective. This work provides important information for the choice of the radius of control surface in the domain decomposition method for solving hydrodynamic problems of body-wave interaction.
KEYWORDS
Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder
Cite this paper
Lv, M. , Li, H. , Ren, H. and Chen, X. (2015) Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder. Journal of Applied Mathematics and Physics, 3, 75-80. doi: 10.4236/jamp.2015.31010.
References
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53587#.VMnhhyzQrzE
Author(s)
Mingdong Lv1, Hui Li1, Huilong Ren1, Xiaobo Chen2
Affiliation(s)
1College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China.
2Bureau Veritas Research Department, Singapore City, Singapore.
ABSTRACT
We consider a vertical circular cylinder on which the vertical variation of water diffraction waves is to be represented by a series of Laguerre functions using Laguerre Polynomials . The variation is assumed to be of the form with the integer n depending on the radius of cylinder. Generally, the integer n increases for a cylinder of larger diameter. The usual approximation by Laguerre functions is extended by introducing a scale parameter. The convergence of Laguerre series is then dependent on the value of the scale parameter s. The analytical and numerical computations of series coefficients are performed to study the number of series terms to keep the same accuracy. Indeed, the choice of integer n depends on the scale parameter. Furthermore, diffraction waves generated by a semi-sphere inside the cylinder are evaluated on the cylinder surface. It is shown that the approximation by Laguerre series for diffraction waves on the cylinder is effective. This work provides important information for the choice of the radius of control surface in the domain decomposition method for solving hydrodynamic problems of body-wave interaction.
KEYWORDS
Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder
Cite this paper
Lv, M. , Li, H. , Ren, H. and Chen, X. (2015) Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder. Journal of Applied Mathematics and Physics, 3, 75-80. doi: 10.4236/jamp.2015.31010.
References
| [1] | Ten, I. and Chen, X.B. (2011) Zero Speed Rankine-Kelvin Hybrid Method. Bureau Veritas Research Department, 6. |
| [2] | Guo, B.-Y. and Wang, Z.-Q. (2007) Numerical Integration Based on Laguerre-Gauss interpolation. Comput. Methods Appl. Mech. Engrg, 196, 3726-3741. http://dx.doi.org/10.1016/j.cma.2006.10.035 |
| [3] | Abramowitz, M. and Stegun, I.A. (1967) Handbook of Mathematical Functions. Dover Publications. eww150129lx |
| [4] | Keilson, J., Nunn, W. and Sumita, U. (1980) The Laguerre Transform. Center for Naval Analysys, 26-28. |
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