Interaction of water waves with an array of vertical cylinders using null-field integral equations

Abstract

The scattering of water waves by an array of vertical circular cylinders is solved by using the null-field integral equations in conjunction with degenerate kernels and Fourier series to avoid calculating the Cauchy and Hadamard principal values. In the implementation, the null-field point can be exactly located on the real boundary owing to the introduction of degenerate kernels for fundamental solutions. An adaptive observer system of polar coordinate is considered to fully employ the property of degenerate kernels. For the hypersingular equation, vector decomposition for the radial and tangential gradients is carefully considered. This method can be seen as a semi-analytical approach since errors attribute from the truncation of Fourier series. Neither hypersingularity in the Burton and Miller approach nor the CHIEF concepts were required to deal with the problem of irregular frequencies. Four gains, well-posed model, singularity free, boundary-layer effect free and exponential convergence are achieved using the present approach. Numerical results are given for the forces and free-surface elevation around the circular boundaries. A general-purpose program for water wave impinging several circular cylinders with arbitrary number, radius, and position was developed. One example of water wave-structure interaction by an array of four bottom-mounted cylinders was demonstrated to see the validity of the present formulation and was compared with those of Linton and Evans, and Perrey-Debain et al.