Commun. Comput. Phys., 6 (2009), pp. 49-71. Fast Numerical Simulation of Two-Phase Transport Model in the Cathode of a Polymer Electrolyte Fuel Cell Pengtao Sun 1*, Guangri Xue 2, Chaoyang Wang 3, Jinchao Xu 41 Department of Mathematical Sciences, University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154, USA. 2 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA. 3 Departments of Mechanical Engineering and Materials Science and Engineering, Electrochemical Engine Center (ECEC), The Pennsylvania State University, University Park, PA 16802, USA. 4 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA; and Laboratory of Mathematics and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China. Received 12 December 2007; Accepted (in revised version) 5 July 2008 Available online 13 November 2008 Abstract In this paper, we apply streamline-diffusion and Galerkin-least-squares finite element methods for 2D steady-state two-phase model in the cathode of polymer electrolyte fuel cell (PEFC) that contains a gas channel and a gas diffusion layer (GDL). This two-phase PEFC model is typically modeled by a modified Navier-Stokes equation for the mass and momentum, with Darcy's drag as an additional source term in momentum for flows through GDL, and a discontinuous and degenerate convection-diffusion equation for water concentration. Based on the mixed finite element method for the modified Navier-Stokes equation and standard finite element method for water equation, we design streamline-diffusion and Galerkin-least-squares to overcome the dominant convection arising from the gas channel. Meanwhile, we employ Kirchhoff transformation to deal with the discontinuous and degenerate diffusivity in water concentration. Numerical experiments demonstrate that our finite element methods, together with these numerical techniques, are able to get accurate physical solutions with fast convergence. AMS subject classifications: 65B99, 65K05, 65K10, 65N12, 65N22, 65N30, 65N55, 65Z05 Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164 Key words: Two-phase model, polymer electrolyte fuel cell, Kirchhoff transformation, convection dominated diffusion problem, streamline diffusion, Galerkin-least-squares. *Corresponding author. Email: pengtao.sun@unlv.edu (P. Sun), xue@math.psu.edu (G. Xue), cxw31@psu.edu (C. Wang), xu@math.psu.edu (J. Xu)