Expansion by Laguerre Function for Wave Diffraction around an Infinite CylinderReport as inadecuate




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We consider a vertical circular cylinder onwhich the vertical variation of water diffraction waves is to be represented bya series of Laguerre functions  using Laguerre Polynomials . The variation is assumed to be of the form  with the integer ndepending on the radius of cylinder. Generally, the integer n increases for acylinder of larger diameter. The usual approximation by Laguerre functions isextended by introducing a scale parameter. The convergence of Laguerre seriesis then dependent on the value of the scale parameter s. The analytical andnumerical computations of series coefficients are performed to study the numberof series terms to keep the same accuracy. Indeed, the choice of integer ndepends on the scale parameter. Furthermore, diffraction waves generated by asemi-sphere inside the cylinder are evaluated on the cylinder surface. It isshown that the approximation by Laguerre series for diffraction waves on thecylinder is effective. This work provides important information for the choiceof the radius of control surface in the domain decomposition method for solvinghydrodynamic problems of body-wave interaction.

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Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder

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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.





Author: Mingdong Lv1, Hui Li1, Huilong Ren1, Xiaobo Chen2

Source: http://www.scirp.org/



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