Scaled boundary FEM solution of short-crested wave interaction with a concentric structure with double-layer arc-shaped perforated cylinders

This paper describes the development of an efficient scaled boundary finite element method (SBFEM) for the solution of short-crested wave interaction with a concentric structure with double-layer arc-shaped perforated cylinders. The arc-shaped cylinders are porous, considered thin in thickness and rigidly fixed on the bottom. As key elements, two virtual closed circular cylinders extending the two arc-shaped cylinders are introduced so that the whole fluid domain is divided into an unbounded and two bounded sub-domains. Furthermore, by supposing the virtual cylinders with variable porosities, the final SBFEM equation is still homogenous and can be also solved semi-analytically. The approach discretises only the outmost cylinder by using the fully analytical characteristics in the radial direction. Based on the SBFEM equation derived from a variational principle manner, the velocity potentials are expressed as a set of independent Hankel functions and Bessel functions for both unbounded and bounded domains, respectively, and the coefficients for those functions are derived in details according to the matching conditions on the boundaries of the two virtual cylinders as well as the Sommerfeld condition. Numerical examples are analyzed to verify the accuracy and demonstrate the efficiency with very few elements. The major factors including wave parameters and structure configurations that affect the wave forces, surface elevations and the diffracted wave contours are examined in details.