A modified method for the singular spatial derivative of velocity potential at corners of 2D bodies and its application to second-order radiation problems

Abstract

For the pressure integration over a body surface, the near-field method is convenient and versatile to calculate all of the wave force components but it is believed to be inferior to the far-field method in precision when calculating the second-order forces. Especially for moving structures with sharp corners, the velocity is singular at corners, which makes higher-order problems difficult. In this paper, analysis on a 2D structural corner is carried out by means of an analytic local solution. The spatial derivative of the velocity potential is modified and calculated to fine accuracy. Furthermore, singular integrations on the body surface are treated elaborately. The components of the second-order forces using the near-field method are presented to show the effect of a singularity. The results are compared with those of the conservative higher-order boundary element method and illustrate high precision. Moreover, the mean drift force obtained from the near-field method is also consistent with that obtained from the middle-field method.