The physics-based method mainly uses Navier-Stokes Equations (NSE) to model fluid motion. According to the different methods of solving NSE, it can be divided into the Eularian method and the Lagrangian method. Eularian method [
11] is a grid-based method [
12]. Although physics-based modeling has greatly increased the physical accuracy of the model, it also has many limitations when simulating large deformation scenes such as overturns and breaks. Therefore, many researchers use the Lagrangian method to simulate large deformation scenes of ocean waves. The Lagrangian method is a particle-based method. It analyzes the movements of individual particles in a fluid, studies the changes in the velocity, pressure, density and other parameters of a given particle in a fluid over time, and studies the changes of parameters when changing from one fluid particle to another fluid particle. In computer graphics, the most commonly used Lagrangian method is the smoothed particle hydrodynamics (SPH) method [
13,
14,
15]. In the SPH method, the physical quantities of fluid particles come from the interpolation of the corresponding physical quantities of other particles in the support domain. The SPH method does not need to layout a grid in the problem domain, so it is not limited by the grid. It also has significant advantages in dealing with large deformation scenes and geometrically complex boundary interaction problems. The SPH method was first introduced into computer graphics by Stam [
16] to simulate fire, smoke, and other gaseous phenomena. Then, Müller [
17] simulated the interactive fluid scenes based on the SPH method for the first time in computer graphics. However, limited by the hardware conditions at that time, the range of fluid scenes is small. Moreover, the incompressibility of the SPH model based on the ideal gas equation of state (EOS) is poor. Subsequently, in computer graphics, most of the SPH literatures focus on the optimization of pressure term to enhance the incompressibility of the model. The study of incompressibility is mainly focused on the treatment of pressure items. In the fluid simulation for computer graphics, there are usually two schemes to deal with the pressure term: the EOS-based methods and the PPE-based (Pressure Poisson equation) methods. Typical EOS-based methods include WCSPH (Weakly Compressible SPH) [
18,
19], PCISPH (Predictive-Corrective Incompressible SPH) [
20], and LPSPH (Local Poisson SPH) [
21]. Among them, PCISPH and LPSPH use a pressure projection scheme, and update pressure iteratively. They allow larger time steps than the WCSPH, which is based on Tait equation. Typical PPE-based methods include ISPH (Incompressible SPH) [
22,
23], IISPH (Implicit Incompressible SPH) [
24], and DFSPH (Divergence-Free SPH) [
25]. The main difference between the PPE-based methods is the source item of PPE. There are currently three common source items: density invariance [
24], velocity divergence [
25], and particle shift [
26]. Compared with the EOS-based method, the PPE-based method has a larger time step and better incompressibility. In fact, EOS-based and PPE-based pressure solving methods are both force-based methods, which update particle velocity through pressure acceleration. Müller et al. [
27] proposed a position-based dynamic (PBD) framework that immediately works on the particle positions. Macklin and Müller [
28] introduced the density constraints [
29] into the PBD framework and named it position-based fluid (PBF). PBF is a very attractive real-time fluid simulation method that allows large time steps and is very stable, and it was adopted by Nvidia’s physical engine, FleX, which has been widely used in various virtual reality scenarios. Based on the concept of PBF, Kang and Sagong [
30] added a set of divergence-free velocity field constraints, called FISPH (Fully Incompressible SPH), but compared with the PBF method, the FISPH method has no obvious speed advantage.
Wind is the motion of air. In aerodynamics, air can be regarded as a Newtonian fluid. Therefore, wind waves are the interactive movement between the two-phase fluids of air and ocean. In the SPH framework, the ideal way is to model the wind waves using the multiphase flow model, but due to the high density ratio, it usually causes stability problems. Moreover, the number of air particles sampled is huge, and the computation is very expensive. Due to the above problems, some researchers try to sample air particles only in the interaction area to save computing resources [
31,
32]. However, these solutions are relatively complicated when managing air particles, so some single-phase solutions [
33,
34,
35] based on drag forces have been proposed, which improves the interaction between air and fluid. The modeling research of high-speed wind field in the SPH framework is still few in computer graphics.
The SPH method also has many applications in simulating certain scale ocean scenes, preferably the wind wave scenes. Akinci et al. [
36] proposed a momentum-conserving two-way fluid-rigid coupling model of SPH fluids, and simulated the scene of a frigate sailing on wavy sea, which is still a state-of-the-art fluid-solid coupling method up to now. Macklin and Müller [
28] simulated the real-time interaction between ocean waves and lighthouse based on the PBF framework. Ihmsen et al. [
24] simulated the scene of a cargo ship in highly agitated ocean using the IISPH method. Bender et al. [
37] proposed a micropolar material model to simulate the turbulent inviscid fluids. They simulated the interaction between ocean and a fast-rotating propeller, and the scenario of a turbulent river flowing through a complex river course. The micropolar fluid method solves the problem of turbulence detail loss caused by the numerical dissipation of the SPH model, and is linear and angular momentum conserving. They then proposed a post-processing model on the basis of the micropolar fluid model to simulate realistic foam effects [
38]. Losasso et al. [
39] proposed a hybrid method that used the particle level set method to model dense liquid volumes and a SPH method to simulate diffuse regions. A large ocean scene with fine-detail mist and foam was simulated using the coupling method.