## 2 Method
### Global Streamline Method  
The streamline method is a commonly used fluid mechanics analysis method, and its principle is inspired by the natural phenomenon of flowing water avoiding obstacles. When  
Figure 1: Global path planning design process. using the streamline method for trajectory planning, the environment is abstracted as a flow field and non-navigable areas are considered obstacles. By simulating fluid movement in the flow field, some streamlines that avoid obstacles can be generated, as shown in Figure 2. The advantage of this method is that the fluid can automatically find the desired outlet and flow out in a given scene due to its global path search capability. This approach avoids the issue of falling into local optimal solutions and is suitable for handling more complex environmental scenes. In addition, due to the flow characteristics of the fluid itself, the final planned route is relatively smooth and meets the restrictions of USV navigation. The article constructs an accurate and reliable chart environment model, calculates the fluid velocity field, and plots the streamlines using fluid dynamic theory, which can find the faster streamlines in the globally feasible solution and provides a reference for route selection. The complexity and variability of maritime navigation conditions result in highly complex wave flows. In order to simplify the model, the following assumptions must be made by selecting the appropriate fluid calculation equations: consider the fluid as inviscid and ignore heat exchange due to viscous forces. The fluid is also assumed to be incompressible and its density is constant, not varying with time or position. Therefore, the fluid satisfies the law of conservation of mass, momentum, and energy. This paper satisfies the following two basic equations:  
Conservation of mass (continuity) equation:  
\[\
abla\cdot(\rho v)=0 \tag{1}\]  
Conservation of momentum equation:  
\[\rho(dv/dt)=-\
abla p \tag{2}\]  
where \(\rho\) is the fluid density, \(v\) is the fluid velocity vector, \(\
abla\) is the gradient operator, \(\cdot\) is the divergence operator, and \((dv/dt)\) is the time derivative of the fluid velocity vector (i.e., the acceleration of the fluid) and its pressure. With the development of high-performance computers, computer simulation is widely used in various fields. CFD uses numerical analysis to simulate fluid flow and calculate fluid forces quickly, accurately, and reliably. Its primary advantage is its ability to find the optimal numerical solutions to nonlinear control equations under complex geometries and boundary conditions. Considering complex hydrodynamic factors, CFD can accurately predict USV motion and response in the ocean, enabling precise route planning. CFD technology is flexible and applicable to different environments and mission requirements, saving the time and resources required to find the optimal navigation strategy for the current situation. In this paper, CFD software is used to simulate the motion state of USVs in a natural marine environment, quickly predict the flow state, and visualize and analyze it in detail, which helps to evaluate the advantages and disadvantages of different routes and guide smarter decisions. Although the streamline method can provide a global solution, its limitation is that the water flow only turns when it encounters an obstacle. It is impossible to predict and avoid obstacles in advance. To overcome this issue, local complex sea areas are divided and planned to ensure the USV can navigate safely and efficiently in regional areas. USVs typically have longer reaction times for collision avoidance and require less precision in their movements in open ocean environments, where obstacles are sparse. On the other hand, more precise  
Figure 2: Principle diagram of streamline method. route planning is required to account for the size and obstacle avoidance requirements of the USV in regions with dense obstacles.