## 3 Numerical Simulations  
### Evaluated FEM Computational Tools  
The numerical simulations of the evaluated LSF walls were performed using four different types of finite elements method (FEM) software: THERM (version 7.8) [29]; FLIXO (version 8.2) [30]; PSIPLAN (version 2024) [31], and ANSYS (student version 2022 R1) [32], where the first three are bi-dimensional (2D), and the last one allows for three-dimensional (3D) models. In the following subsections, some of the details of these software types and the respective numerical models are explained. Starting with the THERM software [29], this is a state-of-the-art computer program, which is being developed in the Lawrence Berkeley National Laboratory, United States  
Figure 2: Implemented methodology scheme. Department of Energy, and makes use of an FEM algorithm to analyse bi-dimensional heat-transfer effects in a steady-state regime. This computational tool creates an automatic mesh for the FEM analysis, which is based on two parameters. The first one is the threshold for the error of the iterative calculations (_\"Maximum % Error Energy Norm\"_), which, in this research, is set at 2%. The second one is the relative size of the finite element mesh of the model (_\"Quad Tree Mesh Parameter\"_), which was set to a standard value of 6. Regarding the definition of boundary conditions, besides the environmental temperatures, this software uses film coefficients (or surface heat transfer coefficients), which are the inverse of the surface thermal resistances. FLIXO software [30] is a finite element analysis computational tool used for assessing 2D thermal bridges in a steady-state. This tool employs four main input features to create an automatic mesh for the implementation of the FEM model. The first is that the mesh can automatically consider the requirements prescribed in standard ISO 10211 [33]. Next, a minimum inside element angle of the triangular shape, set to 20 degrees, is required. After that, a maximum element size should be defined, which was set to 1:150 for this research. Lastly, both maximum values for the relative error and the heat flux error were defined as \(1.0\times 10^{-30}\) and \(1.0\times 10^{-4}\), respectively. Regarding the PSIPLAN 2D [31] software, this was designed to analyze two-dimensional heat transfer within a steady-state thermal regime, employing the plane heat transfer differential equation as its foundational computational model. The input of data is facilitated through a graphical module, offering an intuitive interface for users to define the spatial, geometrical, and thermo-technical characteristics of the subject under investigation. This includes specifying boundary conditions through superficial thermal resistances, interior and exterior temperatures, and relative humidity levels. The program automates the meshing process for thermal bridge junctions by determining the meshing steps according to the specific requirements of the element under study and the simulation's objectives, as outlined in Annex C, subsection C.2.c. of standard ISO 10211 [33]. This process involves formulating equilibrium equations at each node within the mesh, leading to the determination of temperature fields upon the resolution of the equation system. Furthermore, the software adheres to stringent numerical validation criteria for meshing, as detailed in Annex C, subsection C.2. [33]. This section elucidates the methodology for deciding the number of subdivisions and establishes the necessary convergence criteria to ensure the accuracy and reliability of the simulation outcomes. The same discretization network was used for both the homogeneous element case and the inhomogeneous element case, using the same discretization steps and, implicitly, the same total number of discretization axes in the two directions. To enhance the precision of the PSIPLAN simulations, specific attention was paid to the mesh size step, opting for a finer resolution starting from 0.2 mm.