A boundary integral equation method for oblique water-wave scattering by cylinders governed by the modified Helmholtz equation

In this work we are concerned with the interaction of a train of regular deep-water waves with an infinitely long, surface-piercing or submerged cylinder of arbitrary shape (diffraction problem). We are also concerned with the complementary problem of fluid motion induced by the forced oscillations of the cylinder in each of its degrees of freedom: heave, sway, and roll (generalized radiation problem). The amplitude of the oscillation is assumed to vary sinusoidally along the cylinder axis. The problem is solved via the Boundary Integral Equation method by using an appropriate Green function and Green's second identity. According to this method, the initial boundary value problem is formulated as a Fredholm integral equation of the second kind posed on the body boundary. The efficiency of the method depends on the accuracy with which the numerical evaluation of the Green function is performed. For this purpose we employ two alternative representations of the Green function, in conjunction with fast and accurate algorithms for the numerical integration of highly oscillatory functions. Numerical results are presented for a floating semi-circle, a floating inverse T, a submerged circle, and a submerged rectangular cylinder. The efficiency and accuracy of the proposed algorithm is tested with existing results, as well as results for the limiting case of the Laplace equation for which much information is available.