## 5 Conclusions  
In this study, a high-precision CESE solver and immersion boundary layer algorithm (IBM) were used for the first time to couple tunnel structures and methane explosions. The gas deflagration process and wall dynamic response in the approximate real tunnel model and smooth wall tunnel model were studied, and the following conclusions were drawn:  
1. The highest mass fraction of intermediates CH\({}_{3}\) and CH\({}_{2}\)O produced by methane deflagration is much lower than the final product CO\({}_{2}\), and they are almost simultaneously depleted after the complete consumption of methane. At a distance of 1.5 m from the ignition point, the maximum mass fraction of intermediate product CO reaches 4.77%, but CO gas is consumed in large quantities prior to diffusion. At a distance of 1.5-10.5 m from the ignition point, the CO\({}_{2}\) mass fraction reaches 1.29-12.11%.
2. The uneven walls of a tunnel that are approximately real cause changes in the distribution of shock wave overpressure. On straight tunnels, the distribution of shock wave overpressure is asymmetric, with the red high-pressure zone leaning to the right. Meanwhile, the severely uneven tunnel walls decrease the propagation speed and overpressure of the shock wave. Compared with the tunnels with smooth walls, the peak overpressure reduction value of the shock wave reaches 81.91 kPa, and the time when the shock wave overpressure reaches its peak is extended by a maximum of 7.4 ms.
3. The development and diffusion processes of stress loads are close to synchronization with the propagation of shock waves. The propagation speed of stress waves in the bend of the approximate real tunnel is slower than that in the smooth wall tunnel model. Except in the bend tunnel, the positions and ranges of the green stress zone and the red stress concentration zone in the two tunnel models are the same. Compared with smooth-walled tunnels, the stress distribution in the approximate real tunnel is discontinuous, and the transition zone between the green stress zone and the blue unloading zone is serrated, with a shorter duration of high loads.
4. The approximate real tunnel will not lose stability as a result of gas explosion. The displacement of the approximate real tunnel after gas explosion is lower than that in tunnels with smooth walls, and the area of plastic deformation zone is small. The wall displacement of the left tunnel is, at most, 26.9% lower than that of the smooth tunnel. The displacement values of most monitoring points on the right tunnel section are less than half of those in the tunnel with smooth walls.  
These findings prove that the depressions and protrusions on the wall surfaces of underground coal mine tunnels cannot be ignored.  
Conceptualization, J.D.; methodology, J.D.; software, J.D. and X.H.; validation, X.H.; investigation, F.W.; data curation, L.Z.; writing--original draft preparation, L.Z.; writing--review and editing, J.C.; visualization, F.W.; supervision, L.G. All authors have read and agreed to the published version of the manuscript.  
This work was financially supported by the National Natural Science Foundation of China--General Project (52274202), Central Guidance for Local Development Funding Projects (226Z4601G), Natural Science Foundation of Hebei (E2022209051), 2023 Scholarship Program for Introducing Overseas Students (C20230359), Higher Education Youth Top Talent Project of Hebei (BJK2023086), Youth Talent Promotion Program of North China University of Science and Technology (28438101), and Key Scientific Research Project of North China University of Science and Technology (ZD-ST-2022313-23).  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflicts of interest.