Mathematical fuel cell modelling and computational methods for interface problems

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My research areas are mathematical modelling and scientific computation with application to hydrogen fuel cells. Using mathematical modelling, I develop equations that approximately describe the operating fuel cell. The equations are approximate because not all aspects of what is happening in the cell can be included. The resulting equations cannot be solved precisely, but approximate solutions can be found using computers (scientific computing) . We now have a model of an operating fuel cell that can be simulated on a computer. The model is not exact. However, it can be used to investigate how the fuel cell works less expensively than experimental testing. Optimizing fuel cell designs can be done more quickly using the computational model. What the likely failure modes of the fuel cell are and how tolerant the operation is to component tolerances - all these can be modelled computationally. Confidence in the model is only built by comparing it to some experimental measurements. When the model does not match the experiments, the model must be modified (more things not originally included must be added). Some additions to the model involve new mathematics. I work to understand the new terms better analytically. If they appropriately describe the process I want them to describe, I work to figure out how to compute them efficiently. I propose specifically to develop computational models of the start-up of Polymer Electrolyte Membrane hydrogen fuel cells. As hydrogen is introduced into the cell, a situation can exist where there is a reverse current near the air outlet. This current degrades the fuel cell catalyst layer, and is one of the major limitations of fuel cell lifetime in current designs. Capturing this effect in a computational model would allow virtual (fast and inexpensive) testing of mitigation strategies. My main mathematical interest is in understanding models of combined air and water flow in porous media and efficiently computing approximate solutions. The line dividing areas where there is water and where there is only air is known as a free boundary. I am interested in computational methods for general free boundary value problems.