## 3 Numerical Model of Gas Deflagration in Tunnel  
The approximate real tunnel model obtained through 3D modeling is shown in Figure 3. The model mainly includes four parts: a T-shaped tunnel, two-section straight tunnel, and a bend. The walls of the left T-shaped tunnel and straight tunnel have little concave-convex fluctuation. By contrast, the walls of the right straight tunnel and bend are evidently concave-convex and uneven. The straight tunnel and branch tunnel of the T-type tunnel are 11.04 and 9.56 m long, respectively, the widths of the exit end are 2.97 and 2.94 m, and the height is 2.26 m. The straight tunnel connected with the T-shaped tunnel is also 11.04 m long; this tunnel is a transition section, and the rear end width is 2.75 m, which is different from the width of the front end. The length of the second straight tunnel is 13.52 m, and the connected bend includes a 1/4 arc with an inner diameter of 3.63 m and a tunnel section with a length of 1.51 m, with a total length of 9.37 m. The width and height of the tunnel  
Figure 3: Model 1: approximate real tunnel model with uneven tunnel walls. Figure 2: Verification of different gas explosion models based on experimental data. are not fixed due to the evident depressions and protrusions on the right tunnel wall, and the cross-sectional area of the tunnel is between 5.8 m\({}^{2}\) and 5.9 m\({}^{2}\). A tunnel model with smooth walls of the same size is established as a control to clarify the impact of the concave-convex fluctuation of tunnel walls on gas explosion simulation, as shown in Figure 4. The lengths of the straight tunnel, T-shaped tunnel, and bend are consistent with the approximate real tunnel model, but the tunnel walls of the model do not have concave-convex fluctuation. The height and width remain unchanged, and the cross-sectional areas of the tunnels are always 5.88 m\({}^{2}\). The characteristic lengths of small parts, such as the tunnel pipe support, cable, and miner's lamp, are extremely small, greatly increasing the analysis difficulty and calculation time of the numerical model. These small obstacles have a low blockage rate of gas and a limited impact on the shock wave of gas explosion [42]. Therefore, such parts are ignored, and only tunnel and large pipes are reserved. The tunnel walls and pipes are divided by a 2D quadrilateral grid, as shown in Figure 5. The size of the tunnel wall grid transits from 0.05 m in the middle of the straight tunnel to 0.075 m on both sides (19.2 elements/m in the transverse direction of the tunnel; 20.7 elements/m in the vertical direction). The CESE fluid part uses high-quality structured grids, and the computational domain covers the entire tunnel. The fluid grid is divided into two parts: a methane-air mixture and air. The grid size from the combustible-gas part in the middle to the air part transits from 0.045 m to 0.090 m (12.5-18.7 elements/m in the transverse direction of the tunnel; 15.2 elements/m in the vertical direction). The total number of grid elements is 1,451,496. In the CESE fluid element, the position of the ignition point and the distribution of the 9.5% methane-air mixture and air are shown in Figure 6. The ignition point is located in the middle of the whole numerical model. The initial pressure and temperature of the ignition point are 5 bar and 3500 K, respectively. The ignition point is surrounded by the methane-air mixture at normal temperature and pressure, with a length of 6.17 m. The remaining component of the fluid grid is air under normal temperature and pressure conditions and the outflow boundary is set at the exit end of the tunnel. Figure 4: Model 2: tunnel model with smooth walls. For the convenience of analysis, the straight tunnel, T-shaped tunnel, and bend of the approximate real tunnel model and the tunnel model with smooth walls are divided into a-q tunnel sections. The center position of each section of the tunnel is set as the overpressure and gas mass-fraction monitoring point, numbered P1-P17.