# A Multiscale Approach to the Numerical Simulation of the Solid Oxide Fuel Cell
## 1 Introduction
Moreover, methods such as the finite element (FEM) analysis of thermal stresses [22] or the artificial neural networks [23] are employed. The macroscale models are characterized by the low level of modeling details and usually simplified electrochemistry. This approach allows for representing large-scale systems and to analyze the thermo-fluid behavior of the gases inside the cell. On the other hand, the microscale models focus mainly on the analyses of the mass and charge transport within the single electrode or within the PEN (positive electrode-electrolyte-negative electrode) assembly. The microscale models employ a variety of methods, such as the models based on the finite volume solution of partial differential equations [24; 25; 26], the models which implement the Lattice-Boltzmann method (LBM) [27; 28; 29], the sub-grid scale models [30], the random resistor network models [31] or the kinetic Monte Carlo models [32]. A greater amount of modeling details allows for describing the behavior of the electrode very accurately. However, because of the large computational cost, the simulation of the whole cell is a difficult task. Moreover, microscale models usually do not include energy transport. It is possible to combine the macro- and microscale approach and to form a hybrid multiscale model [33], which focuses on the interaction between unit performance and the microstructure of the electrodes. Multiscale models allow for simulating the cell behavior very accurately and to observe the impact of the microstructure on a cell or even a SOFC stack performance. Because of the large complexity and high computational cost, there have been a few attempts to develop the multiscale model. For example, [PERSON] et al. prepared the multiscale model in STAR-CD software (version 3.24, CD-Adapco Group, Melville, NY, USA) [34]. The authors did not mention, from where they took the microstructural data. Moreover, they state that the amount of experimental data needed to confirm the numerical models of the SOFCs are rare in the literature. [PERSON] et al. published a two-dimensional multiscale model of an anode-supported SOFC [35]. The synthetic microstructure is constructed using the random binary packing algorithm and only the electrochemical model is verified with the experimental data. Both models are not used to check the impact of the different microstructure. [PERSON] et al. presented a two-dimensional isothermal model of the PEN [36]. The averaged electrodes' microstructure parameters were taken from thefocused ion beam/scanning electron microscopy (FIB-SEM) measurements, and the set of the experimental results from the short stack is presented. The model does not take into account the flow in the gas channels. As can be seen from the literature review, complex multiscale models are rare and these models are significantly simplified. According to the knowledge of the authors, there is no experimentally confirmed non-isothermal multiscale model, which use a real microstructure data. In this work, we want to develop and to make an attempt to falsify the non-isothermal multiscale model of a single planar SOFC. A mathematical model cannot be proved to be true; however, if the experimental and numerical data are in agreement, the model may be accepted as a verified, which is a goal of the falsification procedure [37]. To reach this aim, we performed the electrochemical tests of the short stack of solid oxide fuel cells to gain a unique set of data. Next, the samples of the analyzed cells' electrodes were observed in three dimensions using the FIB-SEM technique. Collected images are used for the quantification of microstructural parameters, which are implemented into the numerical model. The numerical results from the proposed model are compared with the experimental data. On the basis of the numerical results, we discuss the power generation process in order to achieve a better understanding of the SOFC physics. To demonstrate the importance of the microstructure, the simulation with the different microstructure is provided.