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 3D are carried out to explore and design efficient and robust numerical algorithms for the sake of fast and convergent nonlinear iteration. A more reasonable source term of water transport equation, and a series of efficient numerical algorithms and discretizations are 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) operated by standard finite element/volume method without new numerical techniques.

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