## 3 Numerical Simulation
### Parameter Selection and Model Correctness Verification  
The Reynolds number represents the relationship between inertial force and viscous force, and is the main factor determining the state of the fluid flow. Inertial force plays a primary role at a high Reynolds number; viscous force plays a major role at a low Reynolds number. The expression is:  
\[\text{Re}=\frac{\rho uD}{\mu}=\frac{uD}{\
u} \tag{8}\]  
\(\rho\) is fluid density, \(u\) is fluid velocity, \(D\) is the diameter of the circular cylinder and \(\
u\) and \(\mu\) are the kinematic viscosity and the dynamic viscosity of the fluid, respectively, \(u=\mu/\rho\). The fluid is set to water with a density \(\rho\) = 1000 kg/m\({}^{3}\), and a dynamic viscosity coefficient \(\mu\) = 0.001003 kg/(m\(\cdot\)s). The Strouhal number \(St\) represents the relationship between the cylindrical diameter, the frequency of vortex shedding and the fluid velocity. The expression is  
\[St=\frac{fD}{u} \tag{9}\]  
where  
\(f\) is the frequency of vortex shedding and \(D\) is the diameter of the cylinder. \(C_{\text{I}}\) and \(C_{d}\) are the lift coefficient and the drag coefficient, respectively, whose value depends on the characteristics of the cylinder surface and the Reynolds number. The expression is  
\[C_{\text{I}}=\frac{2F_{\text{I}}}{\rho U^{2}S} \tag{10}\]  
\[C_{d}=\frac{2F_{d}}{\rho U^{2}S} \tag{11}\]  
where \(U\) is the fluid velocity; \(\rho\) is the fluid density; \(S\) is the downstream projection area of the submerged part of the temporary pier; \(F_{\text{I}}\) and \(F_{d}\) are resistance perpendicular to the flow direction and resistance in the downstream direction, respectively, namely the lift and resistance of the cylinder. Table 1 analyzes the influence of the grid size, the influence of the time step on the resistance coefficient and the influence of the Strouhal number when flowing around a single cylinder. The results \(\overline{C_{d}}\) and \(S_{t}\) with a grid size of 0.5 mm are slightly larger than those with grid sizes of 0.2 mm and 0.1 mm. Furthermore, the results of 0.2 mm and  
Figure 2: Calculation domain and grid division. 0.1 mm are close to each other and close to the results of [PERSON] et al., and [PERSON] et al. Considering the precision and efficiency, a grid size of 0.2 mm and a time step of 0.001 s were chosen for subsequent numerical simulations. By comparing with the existing data in the literature, we find that the average resistance coefficient of the calculated value and number are close to the calculated values of [PERSON] ([PERSON], 2003) and [PERSON] ([PERSON] et al., 2010). According to [PERSON]'s ([PERSON] et al., 2010) research, the root mean square (RMS) of the lift coefficient is sensitive to numerical methods, turbulence models and grids, and can be used to capture the periodic characteristics and force action of vortex shedding. As shown in Figure 3, in order to further verify the model correctness, the flow rate range is expanded and compared with the existing literature ([PERSON] et al., 2010; [PERSON] et al., 2010) results to discuss the variation of the order cylinder winding flow at different Reynolds numbers. Due to the direct integral relationship between the lift coefficient and the pressure coefficient, the two dimensionless quantities can be directly verified to obtain a consistent change trend, which shows that the model can simulate the lift situation well with the Reynolds number. As shown in Figure 4, this paper compared the \(S_{t}\) numbers obtained using the method presented in this article with those obtained through experiments conducted by [PERSON] et al., and studied the vortex shedding phenomenon of a cylinder in water. It was found that the two sets of data were in good agreement, further verifying the reliability of the method used in this paper.