## 3 Numerical Simulations
### Model Accuracy Verifications and Validation  
The authors already have a large degree of experience in using three of these computational tools, as can be verified in the following published papers, regarding THERM [18; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40], ANSYS [21; 22; 34; 38; 39; 41; 42] and PSIPLAN [12; 43; 44; 45; 46; 47; 48; 49]. Only the FLIXO software is being used by the authors for the first time, but with excellent results, as can be checked afterwards. Nevertheless, several accuracy verifications and one validation by comparison to measurements were performed. The accuracy verifications that were performed were based on the test cases defined in Annex C of standard ISO 10211 [33], as well as in the analytical calculation procedures defined in standard ISO 6946 [9], for homogeneous layers. Moreover, the implemented models were validated by comparing some results with laboratory measurements under controlled conditions. These verification and validation procedures will be briefly described in the following paragraphs. To ensure the precision of the computational tools used and the models implemented, the first two bi-dimensional test cases prescribed in Annex C of ISO 10211 [33] were simulated, and the following 3D test cases (3 and 4) from the same standard [33] were modelled in ANSYS (the only three-dimensional tested algorithm). The obtained results were within the permitted bounds, the difference between temperatures calculated and listed not exceeding 0.1 \({}^{\circ}\)C and the difference between heat flow values not exceeding 0.1 W/m. The second verification was a comparison of the obtained thermal transmittances for the models previously presented in Figure 1, but simplified (i.e., without steel studs), with the results provided by the analytical calculation procedures provided in standard ISO 6946 [9] for walls with homogeneous layers. The material properties were the ones previously specified in Table 1, and the boundary conditions have also previously been described (please see Section 3.2), the values of the implemented surface thermal resistances being equal to the conventional ones defined in ISO 6946 [9], i.e., 0.13 and 0.04 m\({}^{2}\cdot\)K/W for \(R_{\text{si}}\) and \(R_{\text{se}}\), respectively. Notice that for the partition, we adopted \(R_{\text{se}}\), equal to \(R_{\text{si}}\) (0.13 m\({}^{2}\cdot\)K/W), since both walls' sides are internal (it is a load-bearing partition, instead of a facade). Table 5 displays the overall thermal transmittances obtained for the analytical and numerical approaches, for both types of evaluated walls (simplified partition and facade). \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Iterations** & **1 st** & **2 nd** & **3 rd** & **4 th** & **5 th** & **6 th** & **7 th** \\ \hline \(\phi_{\text{si}}\) (W/model length) & 2.359532 & 2.322598 & 2.318905 & 2.318536 & 2.318499 & 2.318495 & 2.318495 \\ \(\phi_{\text{se}}\) (W/model length) & 2.259720 & 2.312617 & 2.317907 & 2.318436 & 2.318489 & 2.318494 & 2.318495 \\
**Precision** & 0.043215 & 0.004307 & 0.000431 & 0.000043 & 0.000004 & 0.00000 & 0.00000 \\ \hline \(R_{\text{cond}}\) (m\({}^{2}\cdot\)K/W) & 1.526944 & 1.552381 & 1.554969 & 1.555228 & 1.555254 & 1.555257 & 1.555257 \\ \(R\)**-value** (m\({}^{2}\cdot\)K/W) & 1.695252 & 1.722209 & 1.724952 & 1.725227 & 1.725254 & 1.725257 & 1.725257 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation of iterative calculation precision in thermal flux analysis at 0.5 mm subdivision (7546 nodes), regarding the LSF partition PSIPLAN model, for \(R_{\text{si}}\) and \(R_{\text{se}}\) values equal to 0.13 and 0.04 m\({}^{2}\cdot\)K/W, respectively. As expected, for each wall type, the \(U\) values are equal until the third decimal place, ensuring the excellent accuracy of the evaluated algorithms and models. The third strategy to ensure the accuracy of the evaluated LSF wall models was an experimental validation based on laboratory measurements.