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输运问题进行大规模、最先进的模拟。 由于燃料电池数学模型的复杂性，目前的求解方法还远远不能满足要求，因此迫切需要更有效的数值方法。 虽然还有很长的路要走，我们可以有效地解决所有的耦合系统，本建议将致力于解决技术为一个重要的子系统张贴在气体扩散层和气体通道。 这个方程子系统由于各向异性、大的不连续性、简并性和非线性等原因，具有许多临界数值困难。 该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离散化系统，同时解决这些困难。 离散化技术将主要基于自适应有限元/体积法，迭代方法将基于多重网格技术。 离散格式的精度和迭代方法的效率将被研究。燃料电池技术的重要性怎么强调都不过分，因为PEM燃料电池发动机可能在未来取代内燃机。 由于质子交换膜燃料电池同时涉及电化学反应、电流分布、两相流多组分输运和传热，因此需要建立全面的数学模型和计算机模拟，以便：（1）理解许多相互作用的、复杂的、无法通过实验测量的电化学和输运现象;（2）识别限制步骤和组分;（3）模拟车辆行驶条件下的动态响应;（4）为未来更高功率密度（kW/L）、更低成本的燃料电池发动机的设计提供了计算机辅助工具。 PI和co-PI的不同专业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现有的数字代码库，这些代码是由共同PI领导的宾夕法尼亚州电化学发动机中心（ECEC）开发多年的。由于ECEC与国家实验室和汽车制造厂的密切联系，因此，我们希望新的数值技术的发展将导致现有方法的至少一个数量级的改进，自然期望这项研究在国家安全/环境和工业中的应用和影响。此外，这项工作将提供一个独特的跨学科的研究机会，研究生以及本科教育。

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.