## 4 Results and Discussion
### Preliminary Tests  
Several tests were carried out to investigate the grid independence of the FDS results using the four computational grids of Table 2. Using the simplified fire model with \(T_{\text{in}}=1500\) K (Case G-4 in Table 1), results for CO\({}_{2}\) mass flow rate extracted by the ventilation systems, shown in Figure 2a, can be considered fairly grid independent even for the relatively coarse grid \(\Pi\), as well as results for heat flow rate and temperature and CO\({}_{2}\) mass fraction contours on vertical and horizontal sections of the domain (not shown here).  
Figure 2b shows the mass flow rate (positive outwards) through the west and east natural vents and the net mass flow rate leaving the compartment.  
The results depicted in Figure 2b show an acceptable degree of grid independence for grids \(\Pi\) and finer, especially in terms of the net mass flow rate. However, note that the oscillating mass flow rates through the open vents are very sensitive to the grid size, and differences remain between the results obtained with grids \(\Pi\) and \(\Pi\). Indeed, the dependence of these unsteady results on grid size could not be completely avoided unless an extremely fine grid were used. However, the temperature and CO\({}_{2}\) mass fraction contours, the heat and CO\({}_{2}\) mass flow rates through the forced and natural ventilation systems (Figure 2a) and the net mass flow rate leaving the compartment (Figure 2b) do not appreciably change when using grids with \(L/\delta\approx 10,14\) or \(18.5\), and, therefore, the computational grid  
Figure 2: (**a**) Mass flow rates of CO\({}_{2}\) through the ventilation systems and (**b**) mass flow rates through the west and east vents (positive outwards) and net mass flow rate leaving the compartment, obtained with FDS, the simplified fire model with \(T_{\text{in}}=1500\) K (Case G-4 in Table 1) and grids with \(L/\delta\approx 6,10,14\) and \(18.5\).  
with \(L/\delta\approx 10\) (grid II) can be considered sufficiently fine to reach grid independency for the most relevant results. As for the FLUENT code, it was shown in [26] that, for the current scenario, a grid with \(L/\delta\approx 10\) is also fine enough to reach grid independency for the most relevant results. However, the comparison between Figure 2a and the equivalent results shown in [26] shows that FLUENT, when using LES, is more sensitive to the grid size than FDS in predicting, for example, the CO\({}_{2}\) mass flow rate through the forced extraction grilles.  
The Deardorff and Smagorinsky SGS models are the default options for LES models in FDS and FLUENT, respectively [19; 20]. We ran simulations with FDS, using both SGS models, two values for the coefficient \(C_{s}\) of the Smagorinsky model (0.2 and 0.1, the latter being the default value in FLUENT) and two combinations for the turbulent Prandtl and Schmidt numbers (\(\Pr_{t}|\Sc_{t}=0.5|0.5\) and \(0.85|0.7\), which are the default values in FDS and FLUENT, respectively). As in the grid independence test, the results obtained for the mass flow rates through the west and east vents (not shown here) appear to be the most sensitive ones to the settings used for the SGS model (differences for other quantities such as the mass flow rate through the forced extraction grilles and net mass flow rate leaving the compartment are much smaller). Moreover, differences are significant only between the results obtained with FDS and FLUENT, whereas using different settings for the SGS model in FDS does not affect the results substantially.