This paper presents a 2-D real-time modeling approach for a proton-exchange-membrane fuel cell (PEMFC). The proposed model covers multi-physical domains for both fluidic and electrochemical features, which considers in particular the flow field geometric form of fuel cell. The characteristics of reactant gas convection in the serpentine gas pipeline and diffusion phenomenon through the gas diffusion layer (GDL) are thoroughly considered in fluidic domain model. In addition, a three levels iterative solver is developed in order to accurately calculate the implicit spatial physical quantities distribution in electrochemical domain. Moreover, the proposed 2-D real-time modeling approach uses a numerical method to achieve a fast execution time, and can thus be further easily applied to any real-time control implementation or online diagnostic system. After experimental validation under different fuel cell operating conditions, an iterative Least Angle Regression (LAR) method is used to efficiently and accurately perform the global parameters sensitivity analysis based on Sobol definition. The online analysis results give an insight into the influences of modeling parameters on fuel cell performance. The effect of interactions between parameters' sensitivities is especially investigated, which can provide useful information for degradation understanding, parameters tuning, re-calibration of the parameters and online prognostic.