Analysis of Water Wave Problems Containing Single and Multiple Cylinders by Using Degenerate Kernel Method

Abstract

In this paper, water wave problems containing circular cylinders are solved by employing the null-field boundary integral equation in conjunction with degenerate kernels and the Fourier series. The fundamental solution is expanded to the degenerate kernel in the polar coordinates for problems containing circular boundaries. The boundary densities are expanded by using the natural base of the Fourier series. By this means, the field point can be located exactly on the real boundary free of calculating Cauchy and Hadamard principal values. Since errors attribute from the number of terms of the boundary densities, the present method can be seen as a semi-analytical approach. Both single and multiple cylinders are considered. Regarding the case of a single cylinder, our results are compared with those of the boundary element method (BEM) in the literature. The present method achieves higher accuracy and faster convergence than BEM. The near-trapped mode phenomena are observed. The effect of disorder of circular cylinders is also investigated in this paper. Finally, the free-surface elevation of the water wave containing a circular cylinder is animated by using the Mathematica software.