A comprehensive review on accurate numerical simulation of proton exchange membrane fuel cell

PEMFCs involve strongly coupled electrochemical reactions and transport processes of gas, water, charge, and heat. Numerical simulation is therefore an important tool for understanding internal transport phenomena, predicting performance, and supporting PEMFC design and operation. This structured narrative review synthesizes representative PEMFC numerical-simulation studies identified primarily through topic-specific manual searches of the Web of Science database. While many earlier reviews focus on individual processes, components, scales, or modeling routes, the present review connects numerical models from the MEA to macro-scale and multi-scale single-cell models, stack models, operational-process models, system temperature-control models, and efficient-study models based on artificial intelligence and similarity theory. The principal modeling approaches are compared in terms of their physical descriptions, applicable scales, computational costs, validation approaches, and suitable applications. The review shows multi-physics and multiscale models are essential for resolving coupled internal processes, but their effectiveness is constrained by uncertain transport and kinetic parameters, coupling methodology between scales, limited validation data for local physical fields, and high computational cost for large stacks. AI-assisted and reduced-order approaches can improve computational efficiency, but their prediction capability and applicable scale require further development. The review provides a structured summary and outlooks for selecting and improving PEMFC numerical models.