A reaction–convection–diffusion model for PEM fuel cells

Abstract

In this paper, we present a novel 1D singularly perturbed reaction–convection–diffusion mathematical model, with non-linear coefficients (SP-RCD model), for the physical modeling of a fuel cell. The model is a generalization of the macro-homogeneous model, revisited from the point of view of singularly perturbed differential equations. To solve the system of coupled second-order differential equations, we propose a numerical scheme based on vanishing the artificial diffusion of the finite element method within an iterative fixed-point algorithm. We also propose an adaptive Shishkin mesh, as a function of the derivative of the current density in the subdomain with a fast-growing slope. Results of the proposed SP-RCD model are comparable to those of the macro-homogeneous model. In addition, it describes the oxygen concentration profiles in the thickness of the cathode catalytic layer under different operating currents and represents, with enough precision, the experimental polarization curve reported in the literature. • We introduce a novel RCD mathematical model for the numerical simulation of PEM fuel cells. • We introduce a method for stabilizing the numerical solution, it introduces artificial diffusion (AD), until stabilization, then AD is removed. • We introduce a numerical strategy for adapting a Shishkin mesh, avoiding user-made tuning. • Mathematical arguments about convergence are provided. • We validate the algorithm with reported cases and other model.