# The Influence of Mountain Height and Distance on Shape Factor of Wind Load of Plastic Tunnel
## 2 Numerical Simulation Method  
The wall function can directly correlate the uncertainty at the center of the turbulence area with the physical quantities on the wall, and modify the turbulence model by obtaining the values of the nodal variables in the control body. Compared to the Standard Wall Functions, which are more suitable for studying situations wherein the flow near the wall has little impact on the research object, Scalable Wall Functions can be flexibly adjusted according to the thickness of the near wall grid, and generate consistent results for any refined grids. As for our research object, the wind pressure distribution on the surface of the greenhouse is greatly affected by gas flow, and large differences arise between the sizes of the surface grid of the greenhouse and the grid sizes of the mountain. Scalable Wall Functions are chosen in this paper, as they are commonly used for studying fluid flow inside a model [43; 44; 45].  
For both simple and complex flow fields, all fluid dynamics calculations must obey the conservation laws, including energy, mass, and momentum conservation laws, whose relevant expressions are all listed in Reference [46]. When the fluid is turbulent, an additional turbulence equation needs to be added.  
This study evaluates the quality of different turbulence simulations by selecting six different turbulence models for numerical simulation, based on a simple cubic three-dimensional model, and comparing them with the wind tunnel tests conducted by [PERSON] [47] and the results measured on-site by [PERSON] [48], in order to provide a basis for the subsequent simulation analysis. Figure 1 shows the wind pressure distributions calculated by the six different turbulence models at the center of the cube, and compares the simulation results with the results of wind tunnel tests and field tests. Finally, the Realizable \(k-\varepsilon\) model is chosen, which can more effectively match the wind tunnel test and measured results, whether on the simulated windward surface or at the simulated maximum negative pressure [38,39]. The main expression of the Realizable \(k-\varepsilon\) model is as follows:  
\[\frac{\partial(\rho k)}{\partial t}+\frac{\partial(pku_{i})}{\partial x_{i}}= \frac{\partial}{\partial x_{j}}\left[\left(\mu+\frac{u_{i}}{\sigma_{k}} \right)\frac{\partial k}{\partial x_{j}}\right]+G_{k}-p\varepsilon \tag{1}\]  
\[\frac{\partial(\rho\varepsilon)}{\partial t}+\frac{\partial(peu_{i})}{ \partial x_{i}}=\frac{\partial}{\partial x_{j}}\left[\left(\mu+\frac{u_{i}}{ \sigma_{g}}\right)\frac{\partial\varepsilon}{\partial x_{j}}\right]+C_{2}p \frac{\varepsilon^{2}}{k+\sqrt{v\varepsilon}} \tag{2}\]  
In Equations (1) and (2), \(\rho\) is the fluid density; \(k\) is the turbulence kinetic energy, whose expression can be found in Reference [39]; \(\varepsilon\) is the turbulence dissipation ration, whose expression can be found in Reference [39]; \(p\) represents the energy transport term; \(t\) represents time; \(u_{i}\), \(u_{t}\) represent the velocity vector; \(x_{i}\), \(x_{j}\) are the coordinate value; \(\mu\) represents the dynamic viscosity; \(\sigma_{k}\), \(\sigma_{g}\) are the model constants; \(G_{k}\) represents the generation of turbulent kinetic energy caused by the average velocity gradient; \(C_{2}\) is the constant value and equals 1.9; \(\
u\) represents velocity.