## 2 Methods
### Methodology  
First, a CAD geometry has been created for each of the five different 3D models. As can be seen in Figure 1a, the model includes a significant volume of air to establish the conditions of the exterior air contour, and thus to be able to appreciate how it moves as it approaches the facade of the building. The workflow is clearly established from the CFD program. The materials must be assigned for each of the volumes. For the particular case of air, \"moist air\" was selected to perform the hygrothermal simulation. The thermal insulation material used was polystyrene and, for simplicity, the rest of the elements of stony type were assigned the same stone material. The physical properties of the materials used are shown in Table 2.  
Then, the boundary conditions must be assigned. Figure 1a shows the inlet and the outlet for the wind. The rest of the faces of the volume of air have been configured as slip/symmetry to establish the continuity of the model, except for the lower part, which is the floor. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**CASE** & **Dim. Chamber** & **Air Veloc.** & **Joint Dim.** & **Season** & **Direction** \\ \hline
1 & C1: 1 cm & \(\times\)1 & 2 mm & winter & leeward \\
2 & C1: 1 cm & \(\times\)3 & 2 mm & winter & leeward \\ \hline
3 & C3: 3 cm & \(\times\)1 & 2 mm & winter & leeward \\
4 & C3: 3 cm & \(\times\)3 & 2 mm & winter & leeward \\ \hline
5 & C5: 5 cm & \(\times\)1 & 2 mm & winter & leeward \\
6 & C5: 5 cm & \(\times\)3 & 2 mm & winter & leeward \\ \hline
7 & C10: 10 cm & \(\times\)1 & 2 mm & winter & leeward \\
8 & C10: 10 cm & \(\times\)3 & 2 mm & winter & leeward \\ \hline
9 & C25: 25 cm & \(\times\)1 & 2 mm & winter & leeward \\
10 & C25: 25 cm & \(\times\)3 & 2 mm & winter & leeward \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters established for the cases studied. Given that this is a very simple geometric model, automatic mesh sizing was enabled so that the program distributes the nodes and finite elements geometry automatically according to the needs of the model. In this case, a smaller mesh was generated around the 2-mm-thick cladding and joints, with a larger mesh in the external air volume (Figure 2). The model consists of approximately 14 K total nodes (13 K fluid nodes, 1 K solid nodes). The minimum mesh is \(70\times 2\) mm\({}^{2}\) and the maximum mesh \(800\times 800\) mm\({}^{2}\). Similarly, to analyse the case of natural convection in the air chamber, the film coefficients in Table 3 were used. The steady state is of great interest in this case, but not as much the transient state due to the constant temperature gradient that is sought in order to obtain the results. The following physical parameters were considered for the calculation: incompressible flow, hydrostatic pressure, heat transfer, auto forced convection and gravity. The Navier-Stokes mathematical background provides the equations for fluid flow and heat transfer used by the CFD software [36]. The continuity equation can be written as in Equation (1):  
\[\frac{\partial\rho}{\partial t}+\frac{\partial\rho u}{\partial x}+\frac{ \partial\rho v}{\partial y}+\frac{\partial\rho w}{\partial z}=0 \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Moist Air** & **Stone** & **Polystyrene** \\ \hline Density (Kg/m\({}^{3}\)) & incompressible & 2306 & 55 \\ Viscosity (Pa-s) & 0.001817 & - & - \\ Conductivity (W/m K) & 0.02563 & 1.1 & 0.027 \\ Specific heat (J/g K) & 1.004 & 0.837 & 1.21 \\ Emissivity & 1 & 0.92 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical properties of the materials used. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**Flux (W/(m\({}^{2}\)K))**} \\ \hline \multirow{2}{*}{**Horizontal**} & \multicolumn{3}{c}{**Vertical**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Upward**} & \multicolumn{2}{c}{**Downward**} \\ \hline OUT & IN & OUT & IN & OUT & IN \\
4 & 35 & 4 & 35 & 4 & 35 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Film coefficients used in the calculations.