Wave making problems are very important in many applications. Among wave making methods, mass source method is an efficient one. Since the lattice Boltzmann method (LBM) is a simple and efficient numerical method for fluid simulation, we deduct the mass source method based on the Bhatnagar-Gross-Krook (LBGK) form of the lattice Boltzmann method. Free-surface is simulated by single-phase particle level set method (PLSM). The effectiveness of current model is demonstrated by the numerical simulation of a linear wave and a second-order stokes wave. Results show that LBM based mass source method can generate desired waves.
The increasing interest in the seakeeping performance of ships has heightened the need for numerical wave tanks. Various methods have been developed to handle this problem. The most well-known method is the Computational Fluid Dynamics (CFD), which deals with the discrete forms of macroscopic equations, for example, Navier-Stokes equations. Other methods, such as Lattice Boltzmann method (LBM), and smooth particle hydrodynamics (SPH), also show good performance on this problem. Though relatively new, LBM has endured a tremendous development during the last 20 years. As a promising technique for simulating fluid flows, LBM has the following advantages over conventional methods. Firstly, LBM is easily implemented, for it uses a regular, structured grid. Secondly, the collision process of LBM is local, which is very convenient for parallel operations. Thirdly, boundary conditions in LBM can be implemented locally, which means that complex boundaries can be dealt with in an easy way. A challenging for simulating fluid flows using LBM is multiphase flows. Different in complexity, accuracy and computational cost, numerous methods have emerged to handle this problem, including color model (Gunstensen et al., 1991), pseudo-potential model (Shan et al., 1993), free energy model (Swift et al., 1995; Swift et al., 1996), and free-surface (Ginzburg et al.,2003; Thȕrey et al., 2005). However, except the free-surface models, none of these techniques described above can treat multi-phase flows with large density ratio, such as free- surface flows with density ratio near 1000 and so on. Due to the simplicity, high computational efficiency and low memory cost of the free-surface model proposed by Thȕrey (compared with the model by Ginzburg), we will make it as the base model to generate waves in this paper.
