## 3 Fire Scenario
### Computational Grid  
Four different hexahedral computational grids of about 1017 k, 3358 k, 7074 k and 19,864 k cells were used to run the simulations. The grid adaptation capabilities of FLUENT, which facilitate the meshing of complex geometries and local refinement, were not used so that the grid characteristics would be similar when comparing FDS. A uniform cell size in all directions was used for all grids in the region \(0\leq z\leq 2\) m, whereas a grid refinement in \(z\) direction was applied in the vicinity of the ceiling (\(2<z\leq 3\) m) in order to better resolve the flow near the wall. To choose an appropriate order of magnitude for the size of the grid cells, the range of scales that must be resolved to obtain an acceptable accuracy in the results was determined following the criterion that the estimated characteristic length of the fire plume [35],  
\[L=\left(\frac{\text{HRR}}{\rho_{a}c_{p}T_{a}\sqrt{g}}\right)^{2/5}, \tag{4}\]  
should be spanned by at least ten computational cells [28]. For the general scenario conditions described above (\(\text{HRR}=2.5\) MW, \(\rho_{a}=1.17\) kg m\({}^{-3}\), \(c_{p}=1011\) J kg\({}^{-1}\) K\({}^{-1}\) and \(T_{a}=300\) K), we obtain \(L=1.380\) m. In the region \(2<z\leq 3\) m, the cell size in \(z\) direction, \(\Delta z\), gradually shrinks to \(\Delta z_{\text{BL}}\) at the ceiling (\(z=3\) m) in order to ensure suitable values of the parameter \(y^{+}\). Table 2 shows, for each computational grid, the total number of cells, the approximate cell size in the region \(0\leq z\leq 2\) m, \(\delta=\Delta x=\Delta y=\Delta z\), the approximate number of grid cells, \(L/\delta\), spanning the characteristic length \(L\), and the grid size in \(z\) direction at the ceiling, \(\Delta z_{\text{BL}}\). \begin{table}
\begin{tabular}{l l l l l} \hline  & \(\mathbf{T_{in}}\) & \(\mathbf{\dot{\mu_{in}}}\) & \(\mathbf{\dot{\
u_{in}}}\) & \(\mathbf{\dot{\rho_{in}}}\) \\
**Case** & [K] & [\(\mathbf{kg\,s^{-1}}\)] & [\(\mathbf{m\,s^{-1}}\)] & [\(\mathbf{kg\,m^{-3}}\)] \\ \hline G-1 & 2436 & 0.8826 & 2.064 & 0.1429 \\ G-2 & 2124 & 1.052 & 2.145 & 0.1639 \\ G-3 & 1812 & 1.297 & 2.256 & 0.1921 \\ G-4 & 1500 & 1.677 & 2.416 & 0.2320 \\ \hline \end{tabular}
\end{table} 
Table 1: Conditions simulated with the simplified fire model (cases G-1 to G-4), run with Fire Dynamics Simulator (FDS) and FLUENT. Most of the results presented in the following section were obtained using grid II (\(L/\delta\approx 10\)), whereas grids I (coarsest), III and IV (finest) were used for testing grid independence. FDS uses an explicit scheme in time, and automatically adjusts the time step \(\Delta t\) required for numerical stability during the simulation, so that the following condition is met:  
\[\text{CFL}=\Delta t\max\left(\frac{|u|}{\Delta x};\frac{|v|}{\Delta y};\frac{ |w|}{\Delta z}\right)<1. \tag{5}\]  
The default maximum and minimum CFL numbers used by FDS are, respectively, 1 and 0.8. Mean values of \(\Delta t=2.1\) and 1.8 ms were obtained from Equation (5) when using the simplified fire model and the EDC combustion model, respectively. On the other hand, a fully-implicit scheme was used for time advancement in FLUENT, and no stability criterion was taken into account to calculate \(\Delta t\). Instead, we used a constant time step \(\Delta t=50\) ms during the simulations. All residuals diminished by at least two orders of magnitude after around 40 to 50 iterations per time step, and then remained almost constant. The scaled residuals defined in FLUENT [20] for the mass, species, three components of momentum, and energy and radiation equations decreased to around \(10^{-2}\), \(10^{-3}\), \(10^{-4}\) and \(10^{-6}\), respectively. It should be pointed out that, for the same scenario and equivalent simulation settings, FLUENT is considerably more time consuming than FDS, and obtaining strictly time step-independent solutions may require substantially higher CPU times.