A Combined Finite Element-Upwind Finite Volume Method for Liquid-Feed Direct Methanol Fuel Cell Simulations

In this paper, a three-dimensional, two-phase transport model of liquid-feed direct methanol fuel cell (DMFC), which is based on the multiphase mixture formulation and encompasses all components in a DMFC using a single computational domain, is specifically studied and simulated by a combined finite element-upwind finite volume discretization along with Newton's method, where flow, species, charge-transport, and energy equations are simultaneously addressed. Numerical simulations in three dimensions are carried out to explore and design efficient and robust numerical algorithms for the sake of fast and convergent nonlinear iteration. A series of efficient numerical algorithms and discretizations is specifically designed and analyzed to assist in achieving this goal. Our numerical simulations demonstrate that the convergent and correct physical solutions can be attained within 100 more steps, against the oscillating and long-running nonlinear iterations (up to 5000 steps) performed by standard finite element/volume method without new numerical techniques.