International Journal of Scientific & Engineering Research, Volume , Issue 1, -201 ISSN 2229-5518 IJSER © 201 http://www.ijser.org Simulation of the Interaction of Solitary Waves and Breakwaters Using Smoothed Particle Hydrodynamics Mahmoudreza Mollaeinia, Satar Ahmadian, Hamzeh Ebrahimnejadian Abstract— Designing safe and economical seashore structures such as breakwaters is of great importance in the engineering of seashore structures. Besides, breakwaters have a wide variety of applications in commercial and recreational harbors, military activities and offshore operations. In the de- signing process of aforementioned structures, wave rose and wave transmission coefficient are important criteria in determining the height of these structures. Smoothed particle hydrodynamics method is also a powerful tool for studying the free-surface and simulation of waves and structures inter- action. Hence, in the present study, the performance of submerged breakwaters against solitary waves was examined. The main objective of this study was to investigate transmission coefficient of solitary waves in fixed submerged breakwaters. To study the standing waves formed in front of a trapezoid submerged breakwater, a two-dimensional numerical model, without Lagrangian mesh approach and using smoothed particle hydrodynamics method was developed. In this numerical model, solving Navier-Stokes equations are used to investigate the problem. The waves are generated using a piston- type wavemaker which is moving forward. At first, the results of the numerical model were compared to the results of experimental model, and the accu- racy of the model was evaluated. Then the transmission coefficient of solitary waves over the submerged breakwater was studied in different scenarios. Index Terms— Submerged Breakwaters, Solitary Waves, Smoothed Particle Hydrodynamics ——————————  —————————— 1 INTRODUCTION rotecting the coasts against the waves in countries with long coastlines, like Iran, is considered as a serious issue. Also, due to the growth and development of seaports, promenades and coastal installations, using breakwaters for improving water quality is an essential issue. To this end, a variety of coastal structures were built and utilized along the coasts. Submerged breakwater is one of these structures. Sim- ple structure, cost effectiveness, safety for maritime transport vessels, short construction period, retaining the coastal beau- ties for tourism attraction, preventing beach erosion by dis- persing the incoming waves and the high solidity of these structures are among the advantages that can be enumerated for this type of breakwaters. Geometry, the material properties used in the breakwater and environmental features, are among the relevant factors that increase the efficiency of sub- merged breakwaters. In this paper, using the SPH method, the profile of a transmitted wave through a trapezoidal breakwa- ter has been investigated. Following, a number of studies which have been carried out on submerged breakwater are presented. Masanori, et al. (1992) has studied the characteris- tics of solitary wave breaking caused by a submerged obstacle. In this study, the wave breaking rate was calculated using regression method of wave breaking. Norio Hayakawa, et al. (1998), have studied the wave fields around submerged breakwaters using 2-dimentional and 3-dimentional models and compared the results of the empirical method with the results of the theoretical method. Wan Decheng and Wu Guoxiong (1998) have studied solitary wave interaction with a multi bodies breakwater consisted of two rectangular cylin- ders, empirically and theoretically. Akinori Yoshida, et al. (2002) compared the wave field behind a trapezoid submerged breakwater and two trapezoid submerged breakwaters. Ha- keem K. Johnson, et al. (2005) have investigated waves and currents around a trapezoid breakwater empirically and theo- retically. Hong-Bin Chen, et al. (2007) studied wave transfor- mation between trapezoid submerged breakwater and seawall with different profiles empirically. Hasanat Zaman, et al. (2008) investigated the deformation of the monochromatic water wave propagating over a submerged parabolic break- water and the extent of returning wave field in presence of uniform current. Yong-gang Cao, et al. (2010) have carried out a numerical investigation of the hydrodynamic characteristics of water waves propagating around two trapezoid submerged breakwaters. Different methods have been suggested for SPH simulation of waves. Song Dong (2010) has presented the ISPH interaction method with porous environment for water wave simulation. Changen et al. (2011) suggested an optimum SPH method for 3-dimensional wave simulation. 2 THE BASIC GOVERNING EQUATIONS: Smoothed particle hydrodynamic is based on integral interpo- lation. The primary rule is that every function can be approx- imated using the following equation: (1) in which r is position vector of influence point, w is the p 10 IJSER