## 2 Methodology
### Establishment of Simulation Model
The corresponding transport equation is as follows [29]:  
(1) \(k\) equation:  
\[\frac{(\mathrm{pk})}{t}+\frac{\left(\mathrm{p}v_{j}\mathrm{k}\right)}{x_{j}}= \overline{x}_{j}\Bigg{[}\bigg{(}\mu+\frac{\mu_{t}}{\sigma_{k}}\bigg{)}\frac{k }{x_{j}}\Bigg{]}+G_{k}+G_{b}-\rho\varepsilon-Y_{M}+S_{k} \tag{1}\]  
(2) \(\varepsilon\) equation:  
\[\frac{(\rho\varepsilon)}{\mathrm{t}}+\frac{\left(\mathrm{p}v_{j}\varepsilon \right)}{x_{j}}=\overline{x}_{j}\Bigg{[}\bigg{(}\mu+\frac{\mu_{t}}{\sigma_{ \varepsilon}}\bigg{)}\frac{\varepsilon}{x_{j}}\Bigg{]}+\frac{\varepsilon}{k }[c_{1}(G_{k}+G_{b})-c_{2}\rho\varepsilon]+S_{k} \tag{2}\]  
Gk is the term for the generation of turbulent kinetic energy k caused by the average velocity gradient:  
\[G_{k}=\mu_{t}\left(\frac{v_{i}}{x_{j}}+\frac{v_{j}}{x_{i}}\right)\frac{v_{i}} {x_{j}} \tag{3}\]  
Gb is the term for the generation of turbulent kinetic energy k caused by buoyancy:  
\[G_{\mathrm{b}}=-\beta\mu g_{i}\frac{\mu_{t}}{\sigma T}\frac{T}{x_{i}} \tag{4}\]  
YM represents the contribution of pulsation expansion in compressible turbulence. Sk and Se are user-defined source items. C\({}_{\mathrm{\mu}}\) = 0.09, \(\sigma_{\mathrm{K}}\) = 1.0, \(\sigma_{\varepsilon}\) = 1.3, C\({}_{1}\) = 1.44, C\({}_{2}\) = 1.92. Secondly, a simulation model was established based on the actual state of the venue. Because the curling hall of the National Aquatics Center is symmetrical from north to south, only the northern side of the venue was modelled to improve simulation speed, and the overall condition of the venue was simulated by setting up a symmetrical surface [30; 31; 32]. Figure 2 illustrates the establishment of the model. Pixel amplification was performed on the Y-axis coordinate values to ensure clarity in the CFD simulation diagram. The simulation results were compared with the measured results to verify the accuracy of the simulation results, and the corresponding data collection points were established in the model according to field-measured locations [16], as shown in Figure 2b. Points A1, A2, and A3 were located in the lower part of the northern spectator area, middle corridor, and upper part, respectively, representing the air environments at different heights of the spectator area. Point C was located in the competition area, representing the air environment of the competition area. Each collection point was located at a height of 1.5 m from the ground, which was the same height as the measured measurement point. In addition, the bottom floor of the north-west corner of the stadium was adopted as the coordinate origin, the south direction was the positive x-direction, the east direction was the positive y-direction, and the vertical direction was the positive z-direction to establish the coordinate system and reveal the distribution of PM2,5 concentration in the competition and spectator areas of the venue. The section at a distance of 35 m from the origin of the model coordinates in red is called the y = 35 m section. The interface passed through the central area of the ice surface, which displayed the simulation conditions of the spectator and competition areas, as shown in Figure 2c. The World Curling Federation (WCF) proposed a standard for temperature and relative humidity at a height of 1.5 m above the ice surface. Therefore, the 1.5 m section above the ground in the competition area was the simulation interface. The 1.5 m section above the ground on each floor in the spectator area was the simulation interface of the spectator area, as shown in Figure 2d. Finally, the boundary conditions of the model were set, as shown in Table 1, considering the heat exchange of the ice surface and the effects of heat and humidity on the venue [33; 34; 35]. The temperature and relative humidity at the ice surface were determined based on relevant guidelines from the WCF.