This paper presents a numerical investigation on the effects of a second order kernel approximation SPH method (K2_SPH) for modeling nonlinear waves. For the purpose of comparison, three different types of meshless particle approximation methods are tested. The waves generated by two different methods, i.e. piston-type wavemaker and motion of a rectangle tank, are considered. The free surface profiles and velocity distribution are analyzed. These investigations indicate that implement of K2_SPH leads to better prediction of the free surface and velocity distribution.


Nonlinear wave is an important research aspect for marine and ocean engineering. The numerical simulation of these waves still have many great challenges for complex free surface phenomena, such as overturning, breaking and re-entering. Many numerical methods are developed for this purpose. They are divided into mesh-based methods and meshless methods. The mesh-based methods for nonlinear water waves mainly include the boundary element method (Grilli, Guyenne and Dias, 2001), the finite element method (Ma and Yan, 2006; Ma, 2007), the finite difference method(Kishev, Hu, Kashiwagi, 2006)and the finite volume method (Devrard, Marcer, Grilli, Fraunie, and Rey, 2005). A drawback of those methods is that the computation depends on mesh. The mesh may need to be updated repeatedly to follow the motion of the free surface and need to be maintained to have good quality. In the meshless methods, the fluid domain is discretised by particles. They do not need computational mesh and, hence, have high potential to be used for modelling breaking waves. By far, many meshless methods have been reported for the free surface flow simulation, such as Smoothed Particle Hydrodynamics (SPH) (Monaghan, 1994; Lo and Shao, 2002), Meshless Local Petro-Galerkin (MLPG) (Ma, 2005a, b; 2007, Ma and Zhou, 2009), Moving Particle Semi-implicit method (MPS) (Koshizuka and Oka, 1996; Gotoh and Sakai, 2006).

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