## 3 Materials and Methods
### Classroom Case Description
#### 3.5.4 Development of CFD Model for Lecture Room  
1. Model Description  
In this study, the commercial package FLUENT-ANSYS was used to simulate the airflow and airborne aerosols for the lecture room shown in Figure 5. In this regard, a 3-D unsteady state airflow model was developed.  
All the conducted scenarios assume isothermal conditions with a constant air temperature of the order of 20 \({}^{\circ}\)C. The effect of thermal variation was neglected, to reduce the computational time and focus on the other parameters to be investigated, such as the ventilation rate.  
We assumed that the students entered the exam room to take a short-written exam or quiz in all simulations. An instructor who is unaware of being infected is supposed to give the students short verbal instructions related to the exam during the first 3 min while disclosing his/her face mask. We assumed that the oral instructions result in a spread of unified/single aerosol size droplets of 5, 2.5 or 1 \(\upmu\)m that will initially spread out with an initial air velocity of 4.4 m/s and were ejected from the mouth of the infected instructor. For model simplicity, the instructor's mouth was idealized to be rectangular in shape with 2 cm in width and 0.5 cm in height. Some assumptions were previously adopted by other researchers [27; 50].
2. Model Discretization and CGI Analysis  
Figure 6 shows the mesh discretization of the swirl ceiling diffuser. The first layer of grid points on all the students is carefully taken in the near-wall mesh zone to keep the y+ value within an acceptable limit (maximum below 10).  
For the whole class, a mesh of 1,600,000 cells was constructed.  
Numerical models generally use discrete methods to convert the governing partial differential equations into algebraic equations. All discrete methods introduce discretization errors that might be significant enough to ruin the accuracy of the produced numerical solutions. Therefore, the computational fluid dynamics community and many other CFD-reputable journals require discretization error estimation as prerequisites for publishing any CFD paper.  
The grid convergence index (GCI) is a new discretization error estimation technique. The GCI is calculated to answer whether the adopted mesh in the simulation is refined  
Figure 6: Mesh discretization of the swirl ceiling diffuser. (**a**) 2D view. (**b**) 3D view.  
enough or not [51]. A minimum of two mesh solutions is required, but three is recommended to calculate the GCI.  
In the current study, four sizes of meshes depending on the side length of the cells on the students' faces and bodies were tested to calculate the GCI, which were: 10, 8, 6, and 5 cm, where the accuracy of the output results \"the sum of the DPM concentrations on the bodies and the faces of all the students at 90 and 150 s\" is checked. GCI was calculated using the method described in research [51] for the case of no ventilation. GCI fine was less than 1% for mesh 5 cm and less than 1.8% for the mesh of 6 cm. The approximate error was less than 2% for the mesh 5 cm and less than 3.5% for the mesh 6 cm. In this regard, the mesh 5 cm of tetrahedral cells was selected for all further analyses.