Reciprocating compressors represent the most renowned and extensively utilized compressors within the positive displacement category. A compressor that takes input gas at pressures above atmospheric and delivers it very high pressures (> 100 bar) is specifically called a booster pump. These pumps commonly consist of two or more piston-cylinder units in series, connected through check valves that determine the final delivery pressure, and they are instrumental in a range of applications centered around the storage and delivery of gases and fuels. Despite the availability of various booster pumps in the global market, literature offers limited insights into their design specifics. The design intricacies of a booster pump, tailored to operate at specified output pressure and mass flow rate, are contingent upon the interplay of coupled flow dynamics and heat transfer phenomena within the system. These phenomena include fluid flow dynamics through check valves, heat transfer across cylinder walls, and mechanical properties of pump materials, alongside cyclic operational parameters. To address this gap, we have embarked on an experimental-computational investigation aimed at elucidating the transport processes occurring in a single-cylinder booster pump. This work focuses on computational investigations concerning gas compression and the actuation of check valves in a single-cylinder reciprocating booster. Momentum and energy conservation equations were solved on a dynamic mesh platform through Ansys Fluent. Adiabatic conditions were employed, and the numerical solver was partially validated by comparison with thermodynamic theory for simulations conducted in a closed adiabatic cylinder. Calculations were then extended for an open cylinder with inlet and outlet check valves. Simulations indicate that forced cooling plays an important role for the longevity of sealing parts.