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The core of this modelling is to study heat transfer and fluid dynamics processes for a compression expansion system, and the main particularity is that heat transfer and air movement are due to the movement of the piston. We have implemented a "moving mesh" solver to compute the volume changes of the compression chamber followed by a "Fluid dynamics" type solver. It allows correct computation of the fluid behavior in the system and enable us to identify the pressure change of the fluid, and heat generation impacts. The last solver is "heat transfer" solver, to identify the temperature gradient. It is then a strongly non-linear modelling approach. Finally we have plotted corresponding diagrams as they enable us to analyze directly the performance.