## 2 Method
### Numerical Model and Solution Strategies  
To solve the governing equations of fluid flow, heat, and species transport, this investigation used a commercial CFD software program (ANSYS Fluent 19.0). The RANS CFD solved a series of differential equations that can be cast into the general scalar format as:  
\[\frac{\partial}{\partial t}(\rho\phi)+\frac{\partial}{\partial x_{j}}\big{(} \rho u_{i}\phi\big{)}=\frac{\partial}{\partial x_{j}}\bigg{(}\Gamma_{\phi,eff} \frac{\partial\phi}{\partial x_{j}}\bigg{)}+S_{\phi} \tag{2}\]  
where \(\rho\) is the air density, \(\phi\) stands for the velocity component, internal energy, and species concentration in the momentum, energy, and species equations, respectively, \(t\) is time, \(u_{j}\) is the velocity component in three directions (\(x_{j}\), \(j\) = 1, 2, 3) of a Cartesian coordinate system, \(\Gamma_{\phi,eff}\) is the effective diffusion coefficient, \(S_{\phi}\) is the source term. This study adopted the species model to model the airborne pollutant transport, considering that the exhaled  
Figure 3: Model for breathing simulation: (**a**) geometric model of the manikin, (**b**) front view of the manikin head, (**c**) side view of the manikin head, (**d**) breathing cycle. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Cabin air pressure & 85 kPa & Ceiling temperature & 22 \({}^{\circ}\)C \\ Ventilation rate per person & 9.5 L/s & Lighting temperature & 29.4 \({}^{\circ}\)C \\ Width of air-supply opening & 15 mm & Side wall temperature & 22 \({}^{\circ}\)C \\ Air-supply speed & 2.43 m/s & Floor temperature & 23 \({}^{\circ}\)C \\ Air supply direction from the horizontal & 30\({}^{\circ}\) &
\begin{tabular}{c} Manikin skin \\ temperature \\ \end{tabular} & 30.1 \({}^{\circ}\)C \\ Air-supply temperature & 19.4 \({}^{\circ}\)C & Exhalation air temperature & 33 \({}^{\circ}\)C \\ Width of air-exhaust opening & 65 mm & Seat & Adiabatic \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Major thermo-flow boundary conditions. particles commonly ranged from 0.3 \(\upmu\)m to 0.5 \(\upmu\)m [31]. Such ultrafine particles could be simplified as a species of gas. The species fraction was set to 1 at the nostril openings. Most previous investigations [10; 12] used the RNG \(k\)-\(\varepsilon\) model to model the turbulent flows in the aircraft cabin. [PERSON] et al. [32] also recommended the RNG \(k\)-\(\varepsilon\) model for its comparable performance with the RSM model but less computationally demanding in aircraft cabins. Therefore, this investigation adopted the unsteady RNG \(k\)-\(\varepsilon\) model for turbulence simulation. The numerical method uses the SIMPLE algorithm to couple the pressure and velocity equations. The discretization scheme for pressure is PRESTO! The second-order upwind schemes were adopted to discretize the convection and viscous terms of the governing equations. The steady-state airflow pattern in the cabin was resolved first and set as the initial condition for the transient solution. According to [PERSON] et al. [21], the time step should be less than the jet collision cycle. Therefore, this investigation adopted a time step of 0.1 s in the transient simulation. The results were judged to have reached convergence when the relative residuals of all of the independent variables were less than \(10^{-3}\). ANSYS ICEM was used to create the geometry and generate grid meshes. Because of the complexity of the geometric model, this study used the tetrahedral grid scheme. We tested three different grid sizes with a total grid cell number of 6.05 million, 10.09 million, and 18 million. The grid independence analysis results can be found in Figure 11. The grid cell number of 10.09 million was found to provide grid-independent results. The grid cell sizes at the air-supply inlets, manikin surfaces and seats, and the internal space were 10 mm, 25 mm, and 50 mm, respectively. A grid size function with a growth rate of 1.2 was adopted to increase the grid size gradually.