Due to a global shift towards renewable and emission-free energy sources, the need for electrical energy systems is increasing. Fuel cells are important energy systems, as they can convert chemical energy of hydrogen and oxygen into electrical energy, without expelling any environmentally harmful emissions. Especially in electric vehicles and electric aircraft, the combination of a fuel cell system with a hydrogen tank has the potential to become more relevant than batteries, as battery-systems carry a high gravimetric density and scale poorly volumetrically. For a specialized desing of a fuel cell system for vehicles or aircraft, a good understanding of the underlying physics is required. This understanding can be achieved through accurate computational modeling of such systems. The goal of this thesis is to simulate the free flow and porous flow regions of a Polymer Electrolyte Membrane Fuel Cell (PEMFC) using a discontinuous Galerkin approach in Julia. Starting with an already existing implementation of a discontinuous Galerkin simulation of the Euler equations, the computation of the compressible Navier Stokes equations (NSE) is included. These equations require an additional numerical treatment to ensure a stable simulation. Hence, the interior penalty method is implemented for the computation of elliptic partial differential problems. Afterwards, the compressible NSE are coupled with the species equation to obtain the distribution of a chemical species in the flow. To obtain the Darcy-Brinkman-Frorchheimer model for a reactive flow through a porous medium, the simulation is then extended with source terms. The implementation of the compressible NSE is verified for the Taylor-Green problem and the lid-driven cavity flow problem, after which the simulation is used for the evaluation of a gas diffusion layer configuration in a PEMFC.

Keywords: Discontinuous Galerkin Method, Interior Penalty, Compressible NSE, Darcy Equations