Adaptive Multigrid Methods for a Multiphase Fuel Cell Model

The purpose of this project is to develop advanced computational

techniques in order to perform large-scale, state of the art

simulations of two-phase transport problems arising in proton exchange

membrane (PEM) fuel cells. Because of the complexity of the

underlying mathematical models for fuel cells, current solution

techniques are far from being satisfactory, and therefore more

efficient numerical techniques are urgently needed. While there is

still a long way before we can solve all the coupled systems

efficiently, this proposal will be devoted to solution techniques for

an important subsystem posted on the gas diffusion layers and the gas

channel. This subsystem of equations possesses a number of critical

numerical difficulties caused by anisotropy, large discontinuity,

degeneracy and nonlinearity. The goal of the proposed project is to

address these difficulties simultaneously by developing proper

discretization techniques and robust iterative methods for solving the

discretized systems. The discretization techniques to be developed

will be mainly based on adaptive finite element/volume methods and the

iterative methods will be based on multigrid techniques. The accuracy

of the discretization scheme and the efficiency of the iterative

methods for solving the discretized system will be studied.

The importance of the fuel cell technology can hardly be

overemphasized as PEM fuel cell engines can potentially replace

internal combustion engines in the future. Since a PEM fuel cell

simultaneously involves electrochemical reactions, current

distribution, two-phase flow multi-component transport and heat

transfer, comprehensive mathematical modeling and computational

simulation are required in order to: (1) understand the many

interacting, complex electrochemical and transport phenomena that

cannot be measured experimentally; (2) identify limiting steps and

components; (3) simulate dynamic responses under vehicle driving

conditions; and (4) provide a computer-aided tool for design of future

fuel cell engines with much higher power density (kW/liter) and lower

cost. The integration of the different expertise of the PI and co-PI

is expected to lead to significant progress and likely breakthroughs

in the field of fuel cell simulations. Newly developed numerical

techniques will be immediately employed in the existing library of

numerical codes that have been developed for years by the Penn State

Electrochemical Engine Center (ECEC), lead by the co-PI. It is hoped

that the new numerical techniques to be developed will lead to at

least 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 ECEC

with national labs and automobile manufactures. Moreover, this work

will provide a unique interdisciplinary research opportunity for

graduate as well as undergraduate education.