Simulations of interactions between nonlinear waves and multi or an array of cylinders

Abstract

Computational methods are developed to simulate interactions of nonlinear waves with multi-structures through the finite element method based on second order and fully nonlinear theories. The three dimensional (3D) mesh with prism elements is generated through an extension of a two dimensional (2D) unstructured grid. The potential and velocity in the fluid field are obtained by solving finite element matrix equations at each time step using the conjugate gradient method with SSOR preconditioner. The combined Sommerfeld-Orlanski radiation condition and the damping zone method is used to minimize wave reflection. The regridding and smoothing techniques are employed to improve the stability of the solution and the accuracy of the result. The method is first used to simulate interactions of waves and an array of cylinders in the time domain based on the second order theory. Numerical simulations show that the influence of mutual interference between cylinders is highly significant. In particular, the first order and the second order results can become quite large when their corresponding wave number is close to the trapped mode. Simulations based on the fully nonlinear theory are also made for the 3D interactions between fixed multi-cylinders and waves generated by a piston type wave maker in a numerical tank with an artificial beach. Extensive results of practical importance have been obtained, which have been overlooked in many previous applications. The developed method is further employed to solve the 3D fully nonlinear radiation problems by multi-cylinders undergoing large amplitude oscillations in the open sea. All these different applications have clearly demonstrated the flexibility of the method. The simulations also show that the developed method is highly efficient and has great potential to be used for large scale calculation in the motions of floating structures in nonlinear waves.