Finite element simulation of fully non-linear interaction between verticalcylinders and steep waves. Part 1: Methodology and numerical procedure

A methodology for computing three-dimensional interaction between waves and fixed bodies is developed based on a fully non-linear potential flow theor y. The associated boundary value problem is solved using a finite element m ethod (FEM). A recovery technique has been implemented to improve the FEM s olution. The velocity is calculated by a numerical differentiation techniqu e. The corresponding algebraic equations are solved by the conjugate gradie nt method with a symmetric successive overrelaxation (SSOR) preconditioner. The radiation condition at a truncated boundary is imposed based on the co mbination of a damping zone and the Sommerfeld condition. This paper (Part 1) focuses on the technical procedure, while Part 2 [Finite element simulat ion of fully non-linear interaction between vertical cylinders and steep wa ves. Part 2. Numerical results and validation. International Journal for Nu merical Methods in Fluids 2001] gives detailed numerical results, including validation, for the cases of steep waves interacting with one or two verti cal cylinders. Copyright (C) 2001 John Wiley & Sons, Ltd.