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的、目前最先进的模拟。由于燃料电池基础数学模型的复杂性，目前的解决方案技术远远不能令人满意，因此迫切需要更有效的数值技术。虽然我们要有效地解决所有耦合系统还有很长的路要走，但本提案将致力于解决气体扩散层和气体通道上一个重要子系统的求解技术。由于各向异性、大的不连续、退化和非线性等原因，该子系统在数值计算上存在一些困难。提出的项目的目标是通过开发适当的离散化技术和鲁棒迭代方法来解决这些困难，同时解决离散化系统。待开发的离散化技术将主要基于自适应有限元/体积法，迭代方法将基于多网格技术。将研究离散化方案的精度和求解离散化系统的迭代方法的效率。燃料电池技术的重要性怎么强调都不为过，因为PEM燃料电池发动机在未来有可能取代内燃机。由于PEM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传热，因此需要全面的数学建模和计算模拟，以便：(1)理解许多相互作用的、复杂的电化学和传输现象，这些现象无法通过实验测量；(2)确定限制步骤和组成部分；(3)模拟车辆行驶工况下的动态响应；(4)为设计具有更高功率密度（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co-PI的不同专业知识的整合有望在燃料电池模拟领域取得重大进展和突破。新开发的数字技术将立即在现有的数字代码库中使用，这些代码已经由宾夕法尼亚州立电化学引擎中心（ECEC）开发了多年，由co-PI领导。希望即将开发的新的数值技术将导致比现有方法至少一个数量级的改进。由于ececc与国家实验室和汽车制造商的密切联系，这项研究自然会对国家安全/环境和工业产生应用和影响。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.