## 2 Materials and Methods
### CFD Analysis
This made four situations possible: closed window and door (no ventilation), closed window but opened door (internal ventilation which is an indirect ventilation through other spaces that are also being renovated), opened window but closed door (external ventilation) and opened window and door (cross ventilation). In each of them, it was essential to guarantee the continuity of the simulation. For this purpose, an air inlet and outlet opening had to be established. * Scenario 1 (cross-ventilation: Air renewal with opened window and door). Air enters through the window. At the same time, air exits through the door. * Scenario 2 (outdoor-ventilation: Air exchange with opened window and closed door). In this case, the door is closed. The air enters through the window and exists through the lower area of the door (due to its permeability). In this way, continuity is ensured. * Scenario 3 (indoor-ventilation: Air renewal with opened door and closed window). Opposite case to the previous one. * Scenario 4 (no-ventilation: door and window closed). No air is exchanged. In this case, only the concentration of CO\({}_{2}\) metabolically generated by the occupant is simulated. To ensure continuity, it is necessary to define their permeability. The boundary conditions refer to the mass flow of air and CO\({}_{2}\) entering and exiting the room. For the analysis of the renewal of IAQ in the presence of a CO\({}_{2}\) emission source, the geometry was created using DesignModeler, defining the inlets and outlets for each of the gases considered. A turbulent flow was modelled, specifically governed by the equations of the k-omega SST turbulence model. The physico-chemical characteristics of the gases involved were taken from the ANSYS database, activating the \"Species\" model. The composition of exhaled air is 78.6% N\({}_{2}\), 1.8% H\({}_{2}\)O, 15.6% O\({}_{2}\) and 4% CO\({}_{2}\). Accordingly, the mass flux of CO\({}_{2}\) emitted by a person breathing is small. For instance, the amount of air emitted by a person while performing activities at rest is approximately 0.0004 kg/s [91]. This emission was considered to be ideal and constant. Although a mesh with small elements would lead to a more precise solution, this increased the calculation time. This mesh was defined with small triangular elements which were between 0.05 and 0.1 m in size. In addition, the air inlet was considered to be the exterior window opened, and the air outlet was considered to be the interior door opened. To determine the mass flow, the following Equations (1) and (2) were used:  
\[V_{i}=L_{i}\times W_{i}\times H_{i} \tag{1}\]  
where:  
\(V_{i}\) is the volume of the \(scenario_{i}\)  
\(L_{i}\) is the length of the \(scenario_{i}\)  
\(W_{i}\) is the width of the \(scenario_{i}\)  
\(H_{i}\) is the height of the \(scenario_{i}\)  
\[M_{f}=D_{air}\times V_{f} \tag{2}\]  
where:  
\(D_{air}\) is the density of the air at temperature of 25 \({}^{\circ}\)C  
\(M_{f}\) is the Mass flow  
\(V_{f}\) is the Volumetric flow  
Applying the values from the case study:  
\[V=3.9\times 2.4\times 2.5=23.4\;\mathrm{m}^{3},\] \[D_{air}\;(25\;^{\circ}\mathrm{C})=1.3\;\mathrm{Kg/m}^{3}\]  
In the first simulation, cross ventilation: A static analysis was performed in which the gas present in the indoor atmosphere was air. Similarly, for the inlet and outlet opened, the incoming and outgoing gas was also defined as air. For the inlet, the mass flow considered was 0.024 kg/s, which corresponds to three renewals per hour for the volumetric flow. The output of this simulation was defined by the \"outflow\", which allowed the law of conservation of mass to be satisfied: the entire mass flow of air entering through the window passes out the door. In addition, CO\({}_{2}\) was injected, simulating the constant exhalation of a person in a resting state. In the second simulation, outdoor ventilation: The renewal airflow was performed through the window opened (one sliding leaf), the door being closed.