J. Marine Sci. Appl. (2010) 9: 372-378 DOI: 10.1007/s11804-010-1022-5 Simulation of Wave Impact on a Horizontal Deck Based on SPH Method Jia-wen Sun 1 , Shu-xiu Liang 1 , Zhao-chen Sun 1* and Xi-zeng Zhao 2 1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China; 2. RIAM, Kyushu University, Kasuga, Fukuoka 816-8580, Japan Abstract: A numerical model was established for simulating wave impact on a horizontal deck by an improved incompressible smoothed particle hydrodynamics (ISPH). As a grid-less particle method, the ISPH method has been widely used in the free-surface hydrodynamic flows with good accuracy. The improvement includes the employment of a corrective function for enhancement of angular momentum conservation in a particle-based calculation and a new estimation method to predict the pressure on the horizontal deck. The simulation results show a good agreement with the experiment. The present numerical model can be used to study wave impact load on the horizontal deck. Keywords: incompressible smoothed particle hydrodynamics (ISPH); wave impact; kernel gradient correction Article ID: 1671-9433(2010)04-0372-07 1 Introduction 1 Wave impact load on coastal and offshore structures is a major cause of damage to the marine structures. To avoid the damage of those marine structures aroused by the wave impact forces, many laboratory experimental researches have been carried out to estimate the wave impact load (Wang et al., 1970; Kaplan et al., 1992, 1995; Guo and Cai, 1980; Wang et al., 1998; Ren and Wang, 2005; Ren et al., 2007; Zhou et al., 2004). Because the wave impact phenomenon is extremely complicated and involves the strong non-linearity of waves, instantaneous effect, fluid viscosity and turbulence, and the strong interaction between the wave and structure, the progress in research is still unsatisfactory. With the rapid development of computers and computational fluid dynamics, the numerical models based on the Navier-Stokes equations have become popular in the research of wave impact load. Ren and Wang (1999, 2003); Ren et al.,(2007) investigated a numerical wave tank based on improved VOF method to study the wave slamming on a horizontal deck in the splash zone. Kleefsman et al. (2004) put forward an improved VOF method - Comflow using the finite volume method. The free surface is traced using the VOF method together with a local height function, resulting in a strict mass conserving method. The choice of boundary conditions at the free surface appears to be crucial for the accuracy and robustness of the method. Hu and Kashiwagi (2004) applied the CIP method to simulate the wave impact on the structure with quite satisfactory results, Zheng et al. (2009) Received date: 2010-07-01. Foundation item: Supported by the National High Technology Research and Development Program of China (863 Program, Grant No.2007AA11Z130 ). *Corresponding author Email: sunzc@dlut.edu.cn © Harbin Engineering University and Springer-Verlag Berlin Heidelberg 2010 applied the standard ISPH to the study of the interaction between waves and structures, simulated dam collapsing impact pressure on a wall and the wave slamming on a horizontal deck. But the numerical pressure result exhibits large pressure oscillations. The purpose of this paper is to simulate a transient wave impact on a horizontal deck based on an improved ISPH method. The numerical wave impact force results are compared with experimental results by Ren et al. (2003) and numerical results by Zheng et al. (2009). 2 Incompressible SPH model 2.1 Governing equations The N-S equation described by Lagrangian function can be written in the form as follows: 1d 0 d U t ρ ρ +∇⋅ = (1) 2 0 d 1 d U P F U t υ ρ =− ∇ + + ∇ (2) where P = pressure, ρ= density, U=velocity, υ 0 =laminar kinematic viscosity. In the LES framework, Eqs. (1) and (2) in sub-grid scale can be derived from the N-S equation by using a spatial filter and represented as follows: 1d 0 d U t ρ ρ +∇⋅ = (3) 2 0 d 1 1 d U P g U t υ ρ ρ =− ∇ + + ∇ + ∇⋅ τ (4) whereτ stands for sub-grid scale turbulence stresses and are expressed as follows: