## 2 Materials and Methods
### CFD Model Setup
#### 2.5.2 Model Validation  
This section outlines the validation process for the CFD model, which involves comparing the simulation results with experimental data to evaluate the overall quality of the simulation. Validation is essential in every CFD study, as it is the primary method for determining the accuracy and reliability of computational simulations [8]. For this case study, temperature and indoor humidity were selected as evaluation parameters, focusing on a single day, 10 August 2020, which experienced the most extreme atmospheric conditions in terms of temperature and humidity variability compared to all other days during the experimental campaign. The validation was conducted in a stabilized periodic regime to account for the building's thermal inertia and the daily fluctuations caused by the night-day cycle. The average simulated indoor temperature was 30.55 \({}^{\circ}\)C, with a range of \(\pm\)6.25 \({}^{\circ}\)C. In contrast, humidity displayed less variability, remaining relatively stable with a mean value of 54.16% and a range of \(\pm\)4.68%. Comparisons between the numerical simulations and the measured data are presented in Figures 6-8. As can be observed from the figures, the CFD model can reproduce the measured real conditions with good accuracy. The behavior of both the temperature and humidity are in line with the measured trends; the simulation average and maximum errors are reported in Table 5.  
Figure 6: SENSOR 66: comparisons of temperature (**left**) and relative humidity (**right**) measured by the sensor, simulated, and registered outside the building. Figure 7: SENSOR 72: comparisons of temperature (**left**) and relative humidity (**right**) measured by the sensor, simulated, and registered outside the building. Based on the data extracted from the simulations, the average error in the results can be considered as 5% for both temperature and humidity. Based on Table 5, the average errors from the simulation are approximately 2.33 \({}^{\circ}\)C for temperature and 5.38% for relative humidity. Given the relatively high maximum errors, the simulation is better suited to assessing the daily average thermal behavior of the building. These discrepancies may arise from the physical properties of the construction materials (particularly conductivity) being slightly different from their actual values. Notably, the indoor and outdoor measurements exhibit different trends in temperature and relative humidity, indicating that the structure has high thermal inertia. This means that indoor conditions tend to remain stable throughout the day, responding with a delay to external influences. This is expected, considering that the average wall thickness is about 0.6 m, which is typical of many historical buildings [29]. Temperature and relative humidity maps are shown in Figure 9, referencing the time at which humidity peaks. Additional figures (A1 to A3) displaying the velocity vector results and cross-sectional data (humidity, temperature, and velocity) can be found in the Electronic Supplementary Material (ESM). The phenomena of natural convection, wherein the hot air rises, is visible in Figure 9. The section shows natural convective motion, with colder air near the wall and hot air coming from the floor. As visible in the figures, areas with high temperatures have a lower relative humidity and vice versa. This phenomenon, if not managed correctly, can lead to humidity rising from the floor and walls, causing the deposition of dissolved salts where humidity is lower and mold growth where the temperature is higher [30; 31; 32]. Figure 8: SENSOR 84: comparison of temperature (**left**) and relative humidity (**right**) measured by the sensor, simulated, and registered outside the building.