Water wave interaction with surface-piercing porous cylinders using the null-field integral equations

Following the successful experiences of solving water wave scattering problems for multiple impermeable cylinders by the authors' group, we extend the null-field integral formulation in conjunction with the addition theorem and the Fourier series to deal with the problems of surface-piercing porous cylinders in this paper. In the implementation, the null-field point can be exactly located on the real boundary free of calculating the Cauchy and Hadamard principal values, thanks to the introduction of degenerate kernels (or separable kernels) for fundamental solutions. This method is a semi-analytical approach, since errors attribute from the truncation of the Fourier series. Not only a systematic approach is proposed but also the effect on the near-trapped modes due to porous cylinders and disorder of layout is examined. Several advantages such as mesh-free generation, well-posed model, principal value free, elimination of boundary-layer effect and exponential convergence, over the conventional boundary element method (BEM) are achieved. It is found that the disorder has more influence to suppress the occurrence of near-trapped modes than the porosity. The free-surface elevation is consistent with the results of William and Li and those using the conventional BEM. Besides, the numerical results of the force on the surface of cylinders agree well with those of William and Li. Besides, the present method is a semi-analytical approach for problems containing circular and elliptical shapes at the same time.