## 2 Methodology
### Simulation Setup  
The geometry of the subway carriage used in this study is shown in Figure 1a. The dimensions (length \(\times\) width \(\times\) height) of the carriage are 17.34 \(\times\) 2.58 \(\times\) 2.35 m, respectively. The carriage's ventilation system mainly consists of two air conditioning units (not shown) and a ventilation duct system. Each air conditioning unit connects with a supply air inlet and a return air vent. Four windows, six doors, and six seats are symmetrically distributed inside the carriage. The ventilation duct system includes 2 supply air inlets, 2 centralized return air vents, 1 main exhaust air outlet, 12 decentralized exhaust air outlets, and corresponding ducts (supply and exhaust air ducts). In order to replicate the authentic airflow patterns within the carriage, the simulation model retains the complete supply and exhaust air ducts. In the ventilation system, fresh air enters the supply air duct through the supply air inlets and then passes through the supply air grille into the carriage (Figure 1b). A portion of the air inside the carriage circulates through the two central return air vents, while another portion enters the exhaust duct and is concentrated and expelled outside through the roof-mounted total exhaust outlet. The boundary conditions applied to the simulation cases are listed in Table 1. According to the configuration of the air conditioning unit, the total supply and exhaust air rates are 4250 m\({}^{3}\)/h and 2600 m\({}^{3}\)/h, respectively. The volumetric flow rate is converted into the mass flow rate at the supply air inlets and exhaust air outlets. In this study, the subway carriage is assumed to operate in summer, so the carriage and passenger body's surface temperature is set at 35 \({}^{\circ}\)C [64], and the heat transfer coefficient of the vehicle body is set at 2.5 W/(m\({}^{2}\cdot\)K) [65]. All the interior surfaces of the carriage are set as no-slip boundaries. Additionally, to simplify the modeling, the airflow re-entering the carriage from the return air vents is ignored, and the airflow is directly exhausted to the exterior from the return air vents. All the simulations are conducted in the commercial software ANSYS (2022R1) using user-defined functions (UDFs). The simulation scenarios are set up as listed in Table 2. Previous research [15] has shown that the initial droplet size, release velocity, release location, and RH influence the movement characteristics of droplets in confined environments. Among those variables, droplet sizes of 10 \(\upmu\)m, 50 \(\upmu\)m, and 100 \(\upmu\)m are chosen to represent large, medium, and tiny droplets, respectively [41; 66]. Typical initial velocities of 1 m/s and 10 m/s are, respectively, selected to represent the respiratory droplet velocities during breathing and coughing [16; 19]. Given the noticeable differences in the flow characteristics between the positions of D1 and D2, these two positions are selected as the infected passenger positions. Humidity conditions of 35% and 70% are selected to simulate relatively dry and humid air, respectively, according to the relevant literature [41; 67]. Besides these factors, the passenger density inside the subway carriage is also a key parameter, and more research is needed on the impact of passenger density on droplet movement. Therefore, according to the relevant report [68], this study considers two passenger density scenarios: 2 passengers/m\({}^{2}\) (2 p/m\({}^{2}\)) and 4 passengers/m\({}^{2}\) (4 p/m\({}^{2}\)). In the 2 p/m\({}^{2}\) scenario, there are 28 seated passengers and 68 standing passengers; in the 4 p/m\({}^{2}\) scenario, there are 28 seated passengers and 124 standing passengers. The positions of the infected passenger (D1 or D2) and co-passengers in the simulation scenarios are illustrated in Figure 2. Furthermore, according to similar literature [28], when the droplet number is more significant than 10,000, the variance in the droplet number sensitivity is less than 1%.