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

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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.