## 3 Results and Discussion
### The Influence of Train Running Position on the Initial Compression Wave  
4.1 Comparison of the Transition Process of the Initial Compression Wave from Three-Dimensional Wave to One-Dimensional Wave  
Figures 20 and 21, respectively, show the velocity vector distribution at the nose height horizontal cross-section (\(z=0\) m) and the train longitudinal center cross-section (\(y=0\) m) during the process of the head car entering the tunnel. The line integral convolution (LIC) display method is used, with coloring according to the velocity magnitude. At \(t=0\) s, when the train nose enters the tunnel, a strong forward-pushing effect forms in front of the head car. The flow, constrained by the tunnel space, propagates into the tunnel, creating a tunnel compression wave. At this moment, the lateral and rearward displacement effects are relatively weak, resulting in weaker pressure and velocity disturbances that exhibit the characteristics of an expansion wave. As it propagates outside the tunnel, it generates a negative pressure pulse, forming the tunnel entry wave [54]. Not surprisingly, from a spanwise perspective, there are significant differences between offset running and center running cases. The disturbances generated by the offset running are not perpendicular to the flow direction, while the center running maintains a symmetric disturbance pattern. Figure 19: Comparison of the initial compression waves at different points in the \(6 Di\) cross-section: (**a**) pressure–time history curves; (**b**) pressure gradient–time history curves. Figure 18: Comparison of the initial compression waves at different points in the \(5 Di\) cross-section: (**a**) Pressure–time history curves; (**b**) Pressure gradient–time history curves. From a vertical perspective, the disturbances generated by both running modes are similar, exhibiting three-dimensional characteristics. This is attributed to the constraints imposed by the wall surfaces and the ground effect. At \(t=0.0675\) s, the curved portion of the train's nose begins to enter the tunnel. The tunnel walls severely restrict the diffusion of the compressed air. Most of the air compressed by the train continues to move inside the tunnel along the direction of the train's travel, while some of the compressed air escapes through the annular space out of the tunnel. In the spanwise direction, the uneven distribution of the flow field near the train running in an offset case leads to the pressure wave exhibiting three-dimensional characteristics. However, the pressure disturbance farther away from the train already exhibits one-dimensional characteristics. The disturbances generated in the vertical direction by the two operating  
Figure 21: Comparison of the velocity line integral convolution of the \(y=0\) m section colored by velocity magnitude during the process of the head car entering the tunnel. Figure 20: Comparison of the velocity line integral convolution of the \(z=0\) m section colored by velocity magnitude during the process of the head car entering the tunnel. conditions are quite similar, except for a local stagnation area that appears at the top of the tunnel in the centerline running condition (Region A in Figure 21). This local stagnant zone is caused by the airflow flowing towards both sides of the tunnel. At \(t\) = 0.135 s, the streamlined nose of the train is fully inside the tunnel, and the compression wave generated by the nose reaches saturation. The differences in flow disturbances generated by the two operating cases are similar to those at \(t\) = 0.0675 s.  
To compare the influence of the train running position on the three-dimensional characteristics of the compression wave, the pressure iso-surfaces at \(t\) = 0.2025 s are used for visualization. As depicted in Figure 22, high-pressure regions close to the head car have been detected using the pressure iso-surface at 2400 Pa. By comparison, the high-pressure iso-surfaces show significant differences between the offset running and center running cases.