## 4 Discussion  
The use of the volumetric effective properties of porous materials is the state of the art [53]. This is reflected by simulations that use continuum-based approaches for porous regions. These methods are used, e.g., in fuel cell simulations based on commercial CFD software [21; 22; 54]. Other investigations, not only fuel cell related, used open source CFD software [55; 56; 57].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Quantile Level** & \(\mathbf{q}\) & \(\mathbf{s_{\text{tot}}}\) & \(\mathbf{s_{\varnothing}}\) & \(\mathbf{s_{\text{max}}}\) \\ \hline
70\% & 0.78 & 0.75 & 0.43 \\
50\% & 0.70 & 0.81 & 0.34 \\
20\% & 0.65 & 0.42 & 0.46 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Correlation coefficients (Kendall’s method) between the surface characteristics of compressed (30%) and uncompressed GDL.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \(\mathbf{s_{\text{tot}}}\) & \(\mathbf{s_{\text{tot}}}\) \\
**Quantile Level** & \(\mathbf{q}\) & **Uncompressed** & **Compressed (30\%)** \\ \hline
70\% & 28.3\% & 23.6\% \\
50\% & 16.8\% & 13.2\% \\
20\% & 4.9\% & 3.6\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Total quantile areas \(s_{\text{tot}}\) related to the total surface of 590,000 \(\upmu\)m\({}^{2}\), uncompressed and compressed (30%) GDL.  
Domain sizes for the pore-scale simulations of GDLs are often in the mm range [4; 5; 6], while cell and stack simulations require domain sizes of many cm, the size of real fuel cell stacks [21]. The tight coupling of both scales is therefore impossible because of computational resources. The GDL/channel interface was already addressed by PEFC modeling reviews focusing on microfluidics [58] and cell-scale modeling [2]. Some kinds of simulation tasks use boundary conditions at the GDL/channel interface. [PERSON] et al. [1] identified the GDL/channel interface as being of high significance when they discussed two-phase phenomena in PEFCs. The path of further evaluation of the GDL/channel interface depends on its use for upscaling the results to cell-/stack-level simulations. In PNM approaches, the GDL can be represented by regularly-located pores and their characterization by randomly-distributed radii and flow behavior at the interface [35; 37]. This increases the relevance of the knowledge about the sizes and positions of such pores. [PERSON] et al. [59] studied meander-type flow field channels by placing inlet regions on the GDL/channel interface of their PEFC model. Further investigations in the analysis of the exit surface from transport simulations in GDL can improve such cell-level simulations. The combination of this kind of transport simulations leads to multi-scale approaches in fuel cell modeling.  
The approach of analyzing surfaces can potentially also be applied to different simulation techniques. Modeling approaches based on PNM have the potential to cover multiple scales [36; 37], and the interfaces between domains of different spatial scales are of high interest for such investigations. In the field of multi-scale simulations, the presented methods can be a vehicle for combining the simulation domains, especially when domains of different spatial scales are connected.