## 3 Results and Discussion
### The One-Dimensional and Three-Dimensional Characteristics of the Initial Compression Wave  
As shown in Figure 11, at 0 s, the nose tip of the head car just approaches the tunnel entrance, and compression waves generated by the train's movement in the open air have propagated into the tunnel, causing pressure changes. This is consistent with the behavior shown in the pressure-time history curves of the measurement points in Figure 10. The pressure distribution near the train's head inside the tunnel exhibits distinct three-dimensional characteristics. The tunnel wall closer to the train has higher pressure compared to the side away from the train. As depicted in Figure 11b, high-pressure regions close to the head car have been detected using the pressure iso-surface at 800 Pa. Due to limitations imposed by the ground, the tunnel walls, and the curvature of the train's head, this iso-surface exhibits an irregular spherical shape. By employing lower pressures, the pressure iso-surface divides into two parts: one part represents the pressure distribution near the train body, and the other part represents the compression wave in front of the train. It is noteworthy that the pressure iso-surface at 400 Pa capturing the compression wave in front of the train is not perpendicular to the flow direction, presenting an oblique shape. This indicates that it is still influenced by the three-dimensional effect of the head car. However, the pressure iso-surface at 200 Pa capturing the compression wave in front of the train is located further away from the train, and the compression wave surface becomes perpendicular to the flow direction, evolving into a one-dimensional plane wave. To quantitatively analyze the transition of the three-dimensional effect of compression waves to one-dimensional plane waves, the pressure distributions at eight tunnel cross-sections are displayed, ranging from 1_Di_ to 8_Di_ away from the tunnel entrance, as shown in Figure 11c. At the 1_Di_ cross-section, it is evident that the pressure inside the tunnel near the train side is significantly greater than the pressure on the side away from the train, and the maximum pressure is located at the bottom of the tunnel on the right side (near the train). This is mainly due to the compression of air in front of the train caused by its motion, which leads to the air dispersing outward. However, the ground and the tunnel wall near the train restrict the downward and outward flow, causing air accumulation and an increase in pressure. As the cross-sections move farther away from the tunnel entrance, the differences between high-pressure and low-pressure decreases. In the 3_Di_ cross-section, the pressure distribution becomes more even, exhibiting one-dimensional characteristics. As shown in Figure 12, at 0.0675 s, the train's half-nose length enters the tunnel, causing a significant increase in spatial pressure in front of the train. Meanwhile, the pressure difference in the tunnel cross-section near the train increases. In the \(1 Di\) cross-section, the pressure difference exceeds 600 Pa. Similar to the scenario at 0 s, the higher-pressure (1600 Pa) iso-surface represents the high-pressure area near the train's nose, while the lower-pressure iso-surfaces (800 and 400 Pa) represent the pressure distribution around the train and the compression wave in front of the train. In the \(4 Di\) cross-section, the pressure distribution becomes more even, exhibiting one-dimensional characteristics. As shown in Figure 13, at 0.135 s, the entire nose length of the train enters the tunnel, and the spatial pressure in front of the train further increases, approaching saturation. The initial compression wave has fully formed, but it will take some time for the subsequent compression waves to propagate to the measurement point. As depicted in Figure 13b, the initial compression waves captured by the pressure iso-surfaces at 500 and 1000 Pa are both plane waves.