Numerical modelling of wave interaction with a concentric cylindrical system with an arc-shaped porous outer cylinder

The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique, which combines the advantages of the finite element method and the boundary element method. In this paper, the SBFEM is extended to deal with the short-crested wave interaction with a concentric cylindrical system, where the inner cylinder is solid, while the arc-shaped outer cylinder is thin in thickness and porous to protect the interior cylinder. Both cylinders are surface-piercing and fixed on the bottom. As a key element, a virtual circular cylinder extending the arc-shaped porous outer cylinder with the same centre is introduced so that the entire computational domain is partitioned along the virtual cylinder into a bounded domain and an unbounded domain with common interface. Meanwhile, a variable porous-effect parameter GG caused by the complex configuration of the system is introduced for the matching condition of the common interface so that the final SBFEM equation still can be handled in the traditional manner. A new variational principle formulation is used to derive the SBFEM equation in each sub-domain. Hankel functions and Bessel functions are chosen as the basis functions for the solutions of the unbounded and bounded domains, respectively. Then the coefficients for the solutions of the two domains are obtained based on the matching condition. The SBFEM discretizes only the common interface with curved surface finite elements and keeps the radial differential equation solved completely analytically. The results of numerical verification show that the present method yields excellent results with only a few nodes and quick convergence. The effects of the wide range wave parameters and structure configurations including opening angle, position and porous-effect parameter of the outer cylinder as well with the annular spacing on the wave forces, surface elevations and the diffracted wave contours are examined.

► The SBFEM is first applied to wave interaction of a cylindrical system with an arc-shaped porous outer wall.
► A virtual outer cylinder extending the arc-shaped porous outer cylinder is introduced.
► A variable porous-effect parameter GG caused by the complex configuration of the system is introduced.
► We re-derive the solving process for the SBFEM equations.
► The effects of the wide range wave parameters and structure configurations are examined.