TITLE:
Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder
AUTHORS:
Mingdong Lv, Hui Li, Huilong Ren, Xiaobo Chen
KEYWORDS:
Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.1,
January
28,
2015
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.