Applied Ocean Research 67 (2017) 277–290 Contents lists available at ScienceDirect Applied Ocean Research journal homepage: www.elsevier.com/locate/apor Application of smoothed particle hydrodynamics for modeling the wave-moored floating breakwater interaction Bing Ren a,∗ , Ming He b , Yabin Li a , Ping Dong c a The State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China b The State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China c School of Engineering, The Quadrangle, The University of Liverpool, Brownlow Hill, Liverpool L69 3GH, United Kingdom a r t i c l e i n f o Article history: Received 17 January 2017 Received in revised form 6 June 2017 Accepted 19 July 2017 Keywords: Moored floating breakwater Mooring force Wave structure interaction SPH a b s t r a c t The application of a Smoothed Particle Hydrodynamics (SPH) model to simulate the nonlinear interaction between waves and a moored floating breakwater is presented. The main aim is to predict and validate the response of the moored floating structure under the action of periodic waves. The Euler equations together with an artificial viscosity are used as the governing equations to describe the flow field. The motion of the moored floating body is described using the Newton’s second law of motion. The interac- tions between the waves and structures are modeled by setting a series of SPH particles on the boundary of the structure. The hydrodynamic forces acting on the floating body are evaluated by summing up the interacting forces on the boundary particles from the neighboring fluid particles. The water surface ele- vations, the movements of the floating body and the moored forces are all calculated and compared with the available experimental data. Good agreements are obtained for the dynamic response and hydro- dynamic performance of the floating body. The numerical results of different immersion depths of the floating body are compared with that of the corresponding fixed body. The effects of the relative length and the density of the structure on the performance of the floating body are analyzed. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction Floating Breakwaters (FBs) are widely used for damping ocean waves. Compared with traditional bottom mounted breakwaters FBs have many advantages. They can be equally effectively used in offshore or coastal areas with poor foundation. They generally also have relatively less environmental impact and involve short duration of installation and potentially lower construction cost [1]. In development and application of various types of FBs, the forces acting on both the floating breakwater and its mooring lines as well as the dynamic responses of the FB system need to be determined effectively and accurately. The performance of floating structures depends on the interac- tion between the incident waves and the FBs. The early established methods for predicting the performance of moored floating break- waters often use frequency-domain analyses based on potential flow theory [2]. To better deal with the nonlinear wave-structure ∗ Corresponding author. E-mail addresses: bren@dlut.edu.cn (B. Ren), minghe@tju.edu.cn (M. He), dutlyb@163.com (Y. Li), ping.dong@liverpool.ac.uk (P. Dong). interaction, the time domain methods have been developed over the years. The most widely used time domain method is the Mixed Eulerian-Lagrangian (MEL) method introduced by Longuet-Higgins and Cokelet [3] based on Boundary Element Method (BEM). By this method, the instantaneous free surface is treated in the Lagrangian frame and satisfies the nonlinear boundary conditions [4,5]. How- ever, the potential methods neglect the fluid viscosity and are unable to account for the viscous damping which is the dominant damping mode in the pitch motion of a floating body. With the advancement of computational fluid dynamics, a num- ber of numerical simulations based on the NS or RANS equations are carried out to investigate the viscous or turbulent flow involved in the strong nonlinear waves-structure interaction. The NS model combined with VOF method were used to simulated the interaction between waves and inclined-moored submerged floating struc- tures within the frame of Cartesian grid [6,7]. In Rahman’s work [7] the moving boundary of the structure was treated in the Cartesian mesh using FAVOR (Fractional Area/Volume Obstacle Representa- tion) but this treatment suffered from the high computational cost of the mesh generation and re-meshing. Peng [6] applied the IB (Immersed Boundary) method proposed by Peskin [8] to deal with the movable structures. However, the numerical models based on http://dx.doi.org/10.1016/j.apor.2017.07.011 0141-1187/© 2017 Elsevier Ltd. All rights reserved.