Purpose – The purpose of this paper is to describe two- and three-dimensional numerical modelling of solid oxide fuel cells (SOFCs) by employing an accurate and stable fully matrix inversion free finite element algorithm. Design/methodology/approach – A general and detailed mathematical model has been developed for the description of the coupled complex phenomena occurring in fuel cells. A fully matrix inversion free algorithm, based on the artificial compressibility (AC) version of the characteristic-based split (CBS) scheme and single domain approach have been successfully employed for the accurate and efficient simulation of high temperature SOFCs. Findings – For the first time, a stable fully explicit algorithm has been applied to detailed multi- dimensional simulation transport phenomena, coupled to chemical and electrochemical reactions, in fluid, porous and solid parts of a SOFC. The accuracy of the present results has been verified via comparison with experimental and numerical data available in the literature. Originality/value – For the first time, thanks to a stabilization analysis conducted, the AC-CBS algorithm has been successfully used to numerically solve the generalized model, applied in this paper to describe transport phenomena through free fluid channels and porous electrodes of SOFCs, without the need of further conditions at the fluid-electrode interface.
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