A domain decomposition method for two-phase transport model in the cathode of a polymer electrolyte fuel cell

Using Kirchhoff transformation, we develop a Dirichlet–Neumann alternating iterative domain decomposition method for a 2D steady-state two-phase model for the cathode of a polymer electrolyte fuel cell (PEFC) which contains a channel and a gas diffusion layer (GDL). This two-phase PEFC model is represented by a nonlinear coupled system which typically includes a modified Navier–Stokes equation with Darcy’s drag as an additional source term of the momentum equation, and a convection–diffusion equation for the water concentration with discontinuous and degenerate diffusivity. For both cases of dry and wet gas channel, we employ Kirchhoff transformation and Dirichlet–Neumann alternating iteration with appropriate interfacial conditions on the GDL/channel interface to treat the jump nonlinearities in the water equation. Numerical experiments demonstrate that fast convergence as well as accurate numerical solutions are obtained simultaneously owing to the implementation of the above-described numerical techniques along with a combined finite element-upwind finite volume discretization to automatically control the dominant convection terms arising in the gas channel.