Design of Numerical Methods to Simulate Models of a Solid Oxide Fuel Cell

The motivation of this work is to simulate the behavior of a reactive gas mixture in the anode and the overlying gas channel of a solid oxide fuel cell (SOFC). The goal is the identification of loss mechanisms, which limit the performance of the fuel cell, via simulated impedance measurements. Of particular interest are the polarization losses due to gas diffusion in the domain. In order to be able to run efficient numerical simulations of the SOFC, we use model reduction through homogenization as well as goal oriented adaptive mesh refinement, to adjust the solution mechanism to our needs. When stating the mathematical model to describe the processes in the fuel cell, one has to consider the fact that the anode part of the cell consits of a porous medium. This will not be resolved by a numerical grid, as direct simulations on such a complex microstructure are very costly. To overcome this difficulty, effective equations are used. These contain Navier-Stokes and Darcy equation to characterize the flow as well as the Stefan-Maxwell/Dusty-Gas model to describe diffusion and reaction of the species. Over the last years, a lot of work has been put into the coupling conditions of the Navier-Stokes/Darcy system along the interface between fluid and porous region. In 2001, Jaeger, Mikelic and Neuss proposed a set of conditions for the laminar viscous flow over a porous bed, which actually allows to decouple the problem and make it therefor easier to compute. In a first step, these 'decoupling conditions' are compared numerically with a widely used fully coupled approach.