## 3 Numerical Simulations
### Domain Discretization and Boundary Conditions  
As illustrated in Figure 1, only a 400 mm representative width segment of the LSF walls' cross-section was modelled, so as to reduce computation time and effort. The dimensions and thermal conductivities of the materials used in the simulations are displayed in Table 1.  
To perform the numerical simulations, the environmental air temperatures and surface thermal resistances have been defined. In this research, the interior air temperature was set to 20 \({}^{\circ}\)C, while the exterior one was set to 0 and 10 \({}^{\circ}\)C, for the facade and partition LSF walls, respectively. Therefore, the average temperature of the partition LSF walls is 15 \({}^{\circ}\)C, while for the facade LSF walls it is 10 \({}^{\circ}\)C. Table 2 displays the surface thermal resistances adopted. For the internal surface thermal resistance (\(R_{\text{si}}\)), we adopted the default value of 0.13 m\({}^{2}\cdot\)K/W, recommended in standard ISO 6946 [9] for horizontal heat flow. To compare their influence over the computed thermal resistance, six distinct values, ranging from 0 to 0.20 m\({}^{2}\cdot\)K/W, were simulated for the external surface thermal resistance (\(R_{\text{se}}\)). One of these was the ISO-recommended conventional \(R_{\text{se}}\), i.e., 0.04 m\({}^{2}\cdot\)K/W. The conventional surface thermal resistances suggested by ISO 6946 [9] range from 0.04 to 0.17 m\({}^{2}\cdot\)K/W. Thus, we sought to cover this interval, starting at 0.00 (theoretical) and extending up to 0.20 m\({}^{2}\cdot\)K/W. To demonstrate that the mesh configuration and calculation approach employed are sufficiently robust for the simulation, a sensitivity analysis case study for the inhomogeneous partition wall using the PSIPLAN program is here presented. The boundary conditions were \(R_{\text{si}}=0.13\) m\({}^{2}\cdot\)K/W and \(R_{\text{se}}=0.04\) m\({}^{2}\cdot\)K/W, while the interior temperature was 20 \({}^{\circ}\)C and the exterior temperature was 10 \({}^{\circ}\)C. Therefore, the sensitivity analysis was conducted in two stages, as is presented below. The choice of the rectangular discretization network has been validated over the years through the program's development, demonstrating that it provides quick convergence in the resolution of the system of energy balance equations. * _First stage_ The first step was to select a discretization mesh in accordance with criterion C2.d of standard ISO 10211 [33], which mandates that the number of subdivisions should be determined based on a process whereby the sum of the absolute values of all the thermal fluxes entering the object is assessed twice, once for \(n\) nodes (or cells) and then for \(2\times n\) nodes (or cells). The variation between these two assessments must not surpass 1%. If it does, the number of subdivisions must be expanded until the requirement is fulfilled. In the tabulated data presented (see Figure 3 and Table 3), various discretization node counts are employed to elucidate the impact of mesh refinement on the thermal flux, which serves as a critical parameter in the sensitivity analysis. Upon careful scrutiny of the thermal flux alterations consequent to the doubling of discretization nodes, it can be concluded that there is an inverse correlation between the increase in discretization nodes and the percentage deviation in heat flux (\(\phi_{\text{si}}\)). This trend is indicative of the system's convergence characteristics. As can be observed, the condition is met starting from node count of 1739 onwards. Beyond this threshold, any augmentation in node count, characterized by doubling, yields a variance in the calculated thermal flux that is within the permissible limit of less than 1%, thereby affirming the adequacy of the mesh configuration for the thermal simulations conducted. The final row in Table 3 lists the \(R\)-values for all evaluated cases, capturing the impact of thermal bridges on the detailed thermal performance.