## 2 Materials and Methods
### Numerical Simulation Method
#### 2.3.2 Grid Division and Independence Test  
In the actual environment, there are interactions between hydrothermal plumes. To effectively simulate the plume formed by hydrothermal vent groups, a simplified scheme of equivalent vents can be adopted [33]. Specific operations: (1) We assume an axisymmetric three-dimensional space and transform it into a two-dimensional plane computation domain with axisymmetric nozzle. (2) According to the flow equivalence, multiple adjacent active spouts in the active spout group are equivalent to an ideal circular spout. Figure 5a,b shows the detailed mesh size and its partitioning: horizontal radial radius is 1000 m, vertical height is 1000 m, effective radius of vent orifice is 0.1 m, and vent orifice is 2 m above the sea floor.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Vent Office** & **Bottom (Wall)** & **Top** & **Sides** \\ \hline Boundary Condition & Velocity Inlet & No-Slip Boundary & Pressure Outlet & Symmetry Boundary \\ Velocity & w\({}_{\mathrm{exit}}\) = 0.2 m/s & No-Slip (w\({}_{\mathrm{exit}}\) = 0) & Flow in or out the boundary & Zero Gradient \({}^{*}\) \\ Temperature & T\({}_{\mathrm{exit}}\) = 362 \({}^{\circ}\)C & T\({}_{\mathrm{bottom}}\) = 1.74 \({}^{\circ}\)C & T\({}_{\mathrm{top}}\) = 1.9565 \({}^{\circ}\)C & Zero Gradient \({}^{*}\) \\ Dynamic Pressure & \(p\) = 0 & \(p\) = 0 & Constant static pressure & Zero Gradient \({}^{*}\) \\ \hline \hline \end{tabular}  
\({}^{*}\) Zero gradient means that the normal gradient of the physical quantity at the boundary is zero.  
\end{table}
Table 3: Different boundary conditions used in the study.  
The vent orifice is the initial places where hydrothermal fluids erupt, and in order to effectively capture the fine flow of the plume, the mesh of the vent orifice should be treated. Meanwhile, [PERSON] et al. [34] also showed that turbulent mixing near the vent orifice can be correctly reproduced when the mesh size of the area near the vent orifice should be less than D/10 (D is the diameter of the vent orifice). We use the Triangles tool in Fluent to draw the grid. First, the vent orifice radius is evenly divided into 10 equal parts, and then 1/10 of the vent orifice radius is the smallest mesh size (the smallest mesh size is 0.01 m). The grid is set to extend from the vent orifice to the computational domain boundary at a constant expansion rate of 1.02 (Figure 5a).  
In this paper, grid independence test is carried out to verify rationality of grid di-vision  
The maximum plume rising height is the vertical height when the vertical velocity of the plume centerline becomes 0 for the first time. The neutrally buoyant plume height is the vertical height when the density of the plume centerline is equal to the density of the background seawater for the first time.  
It is obvious that the results of Scheme 1 and Scheme 2 are significantly different from those of the other five schemes, which may be caused by insufficient grid detail. The results of the last five schemes of calculation schemes are generally similar, and the differences between the last five schemes are significantly smaller than the differences between the first two schemes. For the maximum plume rising height, the relative difference of the calculated results is less than 0.5%. For the neutrally buoyant plume height, the relative difference among all groups is 1% except Scheme 5. This paper considers that there is a possibility of calculation error in Scheme 5. As can be seen from Figure 6 and Table 4, the corresponding calculation results tend to be stable as the degree of grid division increases. In addition, the increase in the total number of grids in the computing domain also tends to be stable. Therefore, to save time and resources, the design of Scheme 3 (vent orifice 7 equal division) is selected for grid division. Finally, the entire computing domain is discretized by 53,378 triangular elements, as shown in Figure 5b.