## 4 Conclusions  
In this study, three turbulence models (SST k\(-\omega\), SA\(-\)IDDES, and SST\(-\)IDDES) were used to simulate the aerodynamic performance of two MTs passing by each other. The accuracy of the numerical simulation method was verified against the data obtained from the moving model test. The results of the simulations and experimental data showed good agreement. The main conclusions are as follows. Only small differences were found in the transient pressure simulated by different turbulence models. Among them, the differences in the peak-to-peak values of the pressure were found to be less than 5%. When the head and tail cars passed each other, a peak value in the slipstream velocity appeared, and the first peak value was larger than the second. The choice of the turbulence model was found to have a significant effect on the slipstream. The resultant velocity values in the wake calculated with the SST k\(-\omega\) model were significantly lower than those calculated with the SA\(-\)IDDES and SST\(-\)IDDES models. The complex wake flows computed using the different turbulence models were significantly different. Among them, the SA\(-\)IDDES and SST\(-\)IDDES models could capture two main vortices, as well as small-scale vortices. Large amounts of small-scale vortices were obtained with the SST\(-\)IDDES model than with the SA\(-\)IDDES model, specifically in the near-wake region. The SST k\(-\omega\) model failed to capture small-scale vortices. The streamlines projected on the plane were used to analyse the local region of the wake vortex. For the streamlines projected on the plane at the x = 0 position, the vortices on the intersection side of the trains were found to interact, resulting in their weakening. Different turbulence models resulted in a larger difference in the vortex structure on the intersection side but a lower difference in the vortex structure on the non-intersection side. The drag force simulated with the SA\(-\)IDDES model was significantly different from that simulated with the SST k\(-\omega\) and SST\(-\)IDDES models for both head and tail cars, particularly the peak value. For the head car, the largest discrepancy of the maximum absolute value of the drag force was between the SST-IDDES model and SA\(-\)IDDES model, with a difference of 9.3%. For the tail car, the difference between the maximum absolute peak value (SA\(-\)IDDES) and minimum absolute peak value (SST\(-\)IDDES) of the drag force was 4.5%. The turbulence model had little effect on the side force, where the variation trend is consistent and the difference in amplitude is small (less than 6%). The lift force was more sensitive to the choice of turbulence model, particularly that of the tail car. The largest discrepancy in the maximum lift force of the tail car was observed between the SST\(-\)IDDES and SA\(-\)IDDES models, with a difference of 11%. The RANS model is more suitable in terms of the transient pressure, drag and side forces because their values predicted by different models have a small difference, while its computation time is merely about 0.64 times that of the IDDES model based on the k\(-\omega\). If we want to observe changes in the flow field around trains when two MTs passing each other, such as the fluid flow between the train and the track as well as the wake flow, the IDDES model based on k-\(\omega\) is more recommendable because it can capture more small vortices. In future work, more turbulence models will be considered to simulate aerodynamic performance when two MTs passing each other, such as large eddy simulation (LES), embedded large eddy simulation (ELES) and partially\(-\)averaged Navier-Stokes (PANS). X.L. : Conceptualization, software, validation, data curation, writing--original draft preparation; S.K. : methodology, investigation, writing--review and editing; D.Z. : writing--review and editing, supervision, funding acquisition. All authors have read and agreed to the published version of the manuscript.