## 3 Numerical Simulation
### Computation Domain and Boundaries
#### 3.2.3 Measurements and Scheme  
Within the computation domain, a total number of 89 measuring points are mounted in three sets, namely Set A, Set B, and Set C. Set A and B are respectively equipped at tunnel sidewall and train surface to record TPL acting on the tunnel lining and train body. Measuring points in Set C are installed outside the tunnel entrance to detect the micro-pressure. As shown in Figure 6, Set A is divided into eleven sub-sets with each one holding seven measuring points at the same transverse cross-section with different positions, namely PA*-1 to PA*-7. More concretely, PA*-4 locates at tunnel ceiling along  
Figure 5: Different views of multi-meshes.  
tunnel centerline while PA*-1 to PA*-2 and PA*-5 to PA*-7 are respectively mounted at the height of 1.20 m, 2.0 m, and 5.0 m. Symbol \"*\" marked in Figure 5(a) denotes the cross-section number, corresponding to the longitudinal location of each cross-section introduced as below. Along the longitudinal direction, measuring points are placed at \(x_{kin}\) = 10 m, 20 m, 50 m, 100 m, 200 m, 300 m, 400 m, 500 m, 552 m, 592 m, and 602 m. Four measuring points in Set B are respectively placed at train nose, train tail, and two quadratic points at sidewall. Outside the tunnel entrance, micro-pressures at \(x_{lin}\) = 10 m, 20 m, 30 m, 50 m, 75 m, and 100 m along the tunnel centerline and sideway are measured by Set C.  
As shown in Table 1, the present paper conducts 16 numerical simulations with three issues being addressed. Test 1-10 corresponds to the test condition where high-speed train travels through the tunnel. Simulation results from these tests will assist the illustration of flow field and pressure transmission. Higher velocities are designed in Test 5-10 as 450 km/h is likely to be the targeted operating velocity in the high-speed railways in the near future. A 10% surplus addition to the operation speed shall be considered, allowing the upper velocity limit of the simulated train speed being 495 km/h. The intersection of two HSTs are highlighted in Test 11-16 by letting HST running at different velocity levels, i.e., 400 km/h (low speed), 450 km/h (normal speed), and 495 km/h (high speed). Besides, intersection happens in the situation that velocity of Train A being equivalent or different from Train B are both considered to cover the real scenarios that are likely to appear in real tunnels.  
Before the scheduled tests being lunched, validation was first carried out to ensure the accuracy of simulation results. As seen in Figure 7, validation was carried out from two aspects, i.e., mesh sensitivity analysis and comparison with field test data. Simulated data calculated from three meshes with total grid number being 3,209,670 (Grid-1), 4,072,472 (Grid-2), and 4,805,237 (Grid-3) are plotted in Figure 6(a). The plotted curves show very good  
Figure 6: Measuring points in simulations.  
agreement with the maximum pressure difference is only 2.53%, implying that resolution of the present mesh grid is reasonable. Besides, as shown in Figure 7b, history of the MPW obtained from Test 3 in Table 1 and the field test shows good agreement. The maximum pressure difference of MPW caused by HST is only about 3.50 Pa at 50 m away from the tunnel portal. Small fluctuation of pressure wave in the simulated curve is still observed within \(t=0.60\)-1.20 s. However, this is reasonable as (1) the external domain was confined space while the full-scale filed test was conducted in the open space, and (2) train speed in field tests usually fluctuates very often due to many uncertain factors, i.e., tunnel slope and local landform. Overall, the present settings are reasonable to be used for the further simulation.