Efficient numerical techniques of two-phase transport model in the cathode of hydrogen polymer electrolyte fuel cell

该提案是使用2009年美国复苏和再投资法案（公法111-5）提供的资金授予的。本计画旨在发展先进的数值模拟技术，以实现氢质子交换膜燃料电池（PEMFC）阴极两相输运模型的高效、准确及先进的模拟。求解两相输运PEMFC模型的计算效率和精度取决于精确捕捉单相区和两相区各向异性界面的网格划分、适当离散格式的设计以及求解由于扩散系数不连续和退化而引起的高度不稳定非线性系统的有效迭代方法。PI提出了发展各向异性自适应网格技术，以及在离散化和迭代水平上的先进算法，以便设计出更好的离散化模型，可以在最优网格上通过迭代方法更有效和更精确地求解。对于各向异性自适应网格法，PI通过在Hessian矩阵度量下均匀分布有限元边长，提出了一种基于误差均匀分布的后验误差估计器。对于扩散系数的不连续和退化，PI提出了Kirchhoff变换，巧妙地将原PEMFC模型转化为线性泊松方程，并采用Newton方法有效地求解逆Kirchhoff变换。特别地，对于PEMFC中的湿气通道，Kirchhoff变换将不连续性恢复到气体通道与气体扩散层界面上的Kirchhoff变量，PI提出了Dirichlet-Neumann交替迭代区域分解方法来求解该界面边界问题。在离散层次上，PI将设计有限元-迎风有限体积法的组合方法，以克服质子交换膜燃料电池流道内的对流问题，同时又不损失有限元的优点。对于非线性迭代方案，PI将采用皮卡德或牛顿的方法来线性化非线性PEMFC模型，结合特定的预处理Krylov型求解器。PI希望通过将自适应和多层求解的现代数值方法与标准数值方法相结合，对氢质子交换膜燃料电池阴极的两相输运模型进行更有效和更精确的数值模拟。燃料电池被称为安全和可再生能源的关键，例如，燃料电池由于其更高的能量效率和零或超低排放，有望在运输中取代内燃机。质子交换膜燃料电池（PEMFC）是目前最有潜力的燃料电池类型之一，由于PEMFC涉及电化学反应、电流分布、两相流输运和传热等多物理场系统，综合的多物理场系统数学模型和高性能计算与先进的数值计算技术将对燃料电池技术的发展产生重要影响。然而，由于其数学模型的复杂性，目前的数值计算方法在效率和精度上都很不理想。因此，迫切需要先进的数值技术来显着提高燃料电池模拟的效率和精度，本项目提出的数值技术将挑战一些关键的数值困难，这些困难是由大的不连续性，退化，非线性，占主导地位的对流和各向异性，通过设计和分析有效的数值方法，以快速收敛和精确的解决方案。PI将利用所提出的有效的数值方法，最终开发出一个有效的和强大的内部代码PEM燃料电池simulationby实现一个到两个数量级的改善现有的商业燃料电池包的计算性能。PI希望所提出的PEMFC数值技术和数值包将导致计算燃料电池技术领域的重大进展和可能的突破，对燃料电池的商业化产生重大影响，并进一步帮助向氢经济过渡。

This proposal is awarded using funds made available by the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). This project is to develop advanced numerical techniques in order to perform efficient, accurateand state of the art simulations for two-phase transport model in the cathode of hydrogenproton exchange membrane fuel cell (PEMFC). The computational efficiency and accuracy forsolving two-phase transport PEMFC model depends crucially on the partition of mesh for preciselycapturing the anisotropic interface of single- and two-phase zones, the design of properdiscretization schemes and efficient iterative methods for solving a highly unstable nonlinearsystem due to the discontinuous and degenerate diffusion coefficient. The PI proposes to developanisotropic adaptive mesh techniques, and advanced algorithms in both discretizationand iteration level in order to design a better discretized model which can be solved more efficiently and accurately by iterative methods on an optimal mesh. More precisely, for anisotropicadaptive mesh method, the PI proposes an a posteriori error estimator based on error equaldistributionby equalidistributing edge length of finite element in Hessian matrix-metric. For thediscontinuous and degenerate diffusion coefficient, the PI proposes Kirchhoff transformation toskillfully reformulate the original PEMFC model to a linear Poisson's equation, and Newton'smethod to efficiently solve the resulting inverse Kirchhoff transformation. In particular, for thecase of wet gas channel in PEMFC, in which Kirchhoff transformation brings the discontinuityback to the resulting Kirchhoff's variable on the interface of gas channel and gas diffusionlayer, the PI proposes Dirichlet-Neumann alternating iterative domain decomposition methodto resolve this interfacial boundary problem. On the discretization level, the PI will design acombined finite element-upwind finite volume method to overcome the dominant convection ingas channel of PEMFC without losing the benefits of FEM. For nonlinear iteration schemes,the PI will employ either Picard's or Newton's method to linearize nonlinear PEMFC model,combining with specifically preconditioned Krylov-type solver. The PI hopes to develop moreefficient and accurate numerical simulations for two-phase transport model in the cathode ofhydrogen PEMFC by uniting modern numerical techniques of adaptivity and multilevel solverswith standard numerical methods.Fuel cells have been called the key to abundant energy from secure and renewable sources,e.g., fuel cells promise to replace the internal combustion engine in transportation due to theirhigher energy efficiency and zero or ultralow emissions. Hydrogen proton exchange membranefuel cell (PEMFC) is presently considered as a potential type of fuel cells for such application.Since PEMFC involves electrochemical reactions, current distribution, two-phase flow transportand heat transfer, a comprehensive mathematical modeling of multiphysics system and high performancecomputing combining with the advanced numerical techniques shall make a significantimpact in the development of fuel cell technology. However, because of the complexity of the underlyingmathematical model, current numerical techniques are far from being satisfactory dueto poor performances on both efficiency and accuracy. Hence, advanced numerical techniquesare urgently required to significantly improve the efficiency and accuracy of fuel cell simulation.The proposed numerical techniques in this project will challenge a number of critical numericaldifficulties, which are caused by large discontinuity, degeneracy, nonlinearity, dominant convectionand anisotropy, by designing and analyzing the efficient numerical methods toward fastconvergence and precise solutions. The PI will utilize the proposed efficient numerical methodsto eventually develop an efficient and robust in-house code for PEM fuel cell simulationsby achieving one to two orders of magnitude improvement on the existing commercial fuel cellpackages in computational performance. The PI hopes that the proposed numerical techniquesand numerical package for PEMFC will lead to a significant progress and likely breakthrough inthe field of computational fuel cell technology, substantially impacting the commercialization offuel cells and further helping in the transition to hydrogen economy.