Mathematical methods for high resolution modelling of SOFC

For a full understanding of the physics and chemistry of a solid oxide fuel cell, necessary to predict efficiency and durability, the mass flow, current and temperature in the cell have to be modelled with a resolution of a few microns. The talk describes a method to build a three-dimensional mathematical model of an SOFC integrating mass transport by convection and diffusion, chemical reactions, temperature distribution and potentials. The resulting equations may have more than 10^ 5 unknowns for a single cell. They are designed to be solved efficiently by a multigrid method. A preliminary example demonstrating the power of this approach is given