Numerical simulation of fully nonlinear interaction between steep waves and 2D floating bodies using the QALE-FEM method

Abstract

This paper extends the QALE-FEM (quasi arbitrary Lagrangian–Eulerian finite element method) based on a fully nonlinear potential theory, which was recently developed by the authors [Q.W. Ma, S. Yan, Quasi ALE finite element method for nonlinear water waves, J. Comput. Phys, 212 (2006) 52–72; S. Yan, Q.W. Ma, Application of QALE-FEM to the interaction between nonlinear water waves and periodic bars on the bottom, in: 20th International Workshop on Water Waves and Floating Bodies, Norway, 2005], to deal with the fully nonlinear interaction between steep waves and 2D floating bodies. In the QALE-FEM method, complex unstructured mesh is generated only once at the beginning of calculation and is moved to conform to the motion of boundaries at other time steps, avoiding the necessity of high cost remeshing. In order to tackle challenges associated with floating bodies, several new numerical techniques are developed in this paper. These include the technique for moving mesh near and on body surfaces, the scheme for estimating the velocities and accelerations of bodies as well as the forces on them, the method for evaluating the fluid velocity on the surface of bodies and the technique for shortening the transient period. Using the developed techniques and methods, various cases associated with the nonlinear interaction between waves and floating bodies are numerically simulated. For some cases, the numerical results are compared with experimental data available in the public domain and good agreement is achieved.