Stirling engines (SEs) have long attracted the attention of renewable energy researchers due to their external combustion design and flexibility in operating with various heat sources. The mathematical analysis of these devices is conducted by using a broad range of models ranging from basic zero-order to highly detailed fourth-order models, which are implemented through Computational Fluid Dynamics (CFD) simulations. The unique features of this last approach, combined with the increase in computing power, have promoted the use of CFD as a tool for analyzing SEs in recent years, significantly reducing the costs associated with prototype construction. However, Stirling CFD simulations are sophisticated due to the variety of physical phenomena involved, such as volume change, conjugated heat transfer, turbulent compressible fluid dynamics, and flow through porous media in the regenerator. Furthermore, there is currently no comprehensive review of CFD simulations of SEs in the literature; therefore, this contribution aims to fill that gap. Emphasis has been placed on identifying the type of engine, the physical phenomena modeled, the simplifying assumptions, and specific numerical aspects, such as mesh type, spatial and temporal discretization, and the order of the numerical schemes used. As a result, it has been found that in many cases, CFD numerical reports lack sufficient detail to ensure the reproducibility of the simulations. This work proposes guidelines for reporting CFD studies on Stirling engines to address this issue. Additionally, the need for a sufficiently detailed experimental benchmark database to validate future CFD studies is stressed. Finally, the use of Large Eddy Simulations on coupled key engine components—such as compression and expansion spaces, pistons, displacer, and regenerator—is suggested to provide further insights into the specific flow and heat transfer characteristics in Stirling engines.
