A Numerical Solution of Two-Dimensional Deep Water Wave-Body Problems

Abstract

A numerical technique is presented for the solution of deep water linear and time-harmonic wave-body-interaction problems in two dimensions. A mathematical boundary of circular shape surrounding the body is introduced in the fluid domain, thus defining two flow regions. A multipole expansion valid in the outer region is then matched to an integral representation of the solution in the inner region which is obtained by applying Green's theorem and by using the fundamental logarithmic singularity as the Green function. The method applies both to surface-piercing and submerged bodies. Numerical results are presented for the forced oscillations of three surface-piercing ship-like sections of regular shape. No irregular frequencies are encountered. Comparisons with existing numerical methods are made to test the accuracy and emphasize the computational efficiency of the present approach.