Adaptive Multigrid Methods for a Multiphase Fuel Cell Model

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The purpose of this project is to develop advanced computationaltechniques in order to perform large-scale, state of the artsimulations of two-phase transport problems arising in proton exchangemembrane (PEM) fuel cells. Because of the complexity of theunderlying mathematical models for fuel cells, current solutiontechniques are far from being satisfactory, and therefore moreefficient numerical techniques are urgently needed. While there isstill a long way before we can solve all the coupled systemsefficiently, this proposal will be devoted to solution techniques foran important subsystem posted on the gas diffusion layers and the gaschannel. This subsystem of equations possesses a number of criticalnumerical difficulties caused by anisotropy, large discontinuity,degeneracy and nonlinearity. The goal of the proposed project is toaddress these difficulties simultaneously by developing properdiscretization techniques and robust iterative methods for solving thediscretized systems. The discretization techniques to be developedwill be mainly based on adaptive finite element/volume methods and theiterative methods will be based on multigrid techniques. The accuracyof the discretization scheme and the efficiency of the iterativemethods for solving the discretized system will be studied.The importance of the fuel cell technology can hardly beoveremphasized as PEM fuel cell engines can potentially replaceinternal combustion engines in the future. Since a PEM fuel cellsimultaneously involves electrochemical reactions, currentdistribution, two-phase flow multi-component transport and heattransfer, comprehensive mathematical modeling and computationalsimulation are required in order to: (1) understand the manyinteracting, complex electrochemical and transport phenomena thatcannot be measured experimentally; (2) identify limiting steps andcomponents; (3) simulate dynamic responses under vehicle drivingconditions; and (4) provide a computer-aided tool for design of futurefuel cell engines with much higher power density (kW/liter) and lowercost. The integration of the different expertise of the PI and co-PIis expected to lead to significant progress and likely breakthroughsin the field of fuel cell simulations. Newly developed numericaltechniques will be immediately employed in the existing library ofnumerical codes that have been developed for years by the Penn StateElectrochemical Engine Center (ECEC), lead by the co-PI. It is hopedthat the new numerical techniques to be developed will lead to atleast an order of magnitude improvement over the existing methods.Application and impact to national security/enviroment and to industries are naturally expected for this research because of the close tie of ECECwith national labs and automobile manufactures. Moreover, this workwill provide a unique interdisciplinary research opportunity forgraduate as well as undergraduate education.