Adaptive Multigrid Methods for a Multiphase Fuel Cell Model

该项目的目的是开发先进的计算技术，以便对质子交换膜(PEM)燃料电池中出现的两相传输问题进行大规模、最先进的模拟。由于燃料电池基本数学模型的复杂性，目前的求解技术远远不能令人满意，因此迫切需要更有效的数值技术。虽然要有效地求解所有耦合系统还有很长的路要走，但这项建议将致力于解决位于气体扩散层和气体通道上的一个重要子系统的求解技术。由于各向异性、大间断性、简并性和非线性，这一方程子系统具有许多临界数值困难。该项目的目标是通过发展离散化技术和用于求解离散系统的稳健迭代方法来同时解决这些困难。拟发展的离散化技术将主要基于自适应有限元/体积方法，迭代方法将基于多重网格技术。对离散格式的精度和求解离散系统的迭代方法的效率进行了研究，燃料电池技术的重要性怎么强调都不为过，因为质子交换膜燃料电池发动机在未来有可能取代内燃机。由于质子交换膜燃料电池同时涉及电化学反应、电流分布、两相流多组分传输和热传递，因此需要全面的数学建模和计算模拟，以便：(1)了解许多无法通过实验测量的相互作用、复杂的电化学和传输现象；(2)确定限制步骤和组件；(3)模拟车辆驾驶条件下的动态响应；以及(4)为设计更高功率密度(kW/L)和更低成本的未来燃料电池发动机提供计算机辅助工具。PI和共同PIIs的不同专门知识的整合预计将导致燃料电池模拟领域的重大进展和可能的突破。新开发的数字技术将立即用于由宾夕法尼亚州立大学电化学发动机中心(ECEC)领导的现有数字代码库，该库已开发多年。由于ECEC与国家实验室和汽车制造商的密切联系，这项研究的应用和对国家安全/环境和行业的影响自然是意料之中的。此外，这项工作将为研究生和本科教育提供一个独特的跨学科研究机会。

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.