The objective of this paper is to complete a thorough investigation of the pressure wave supercharger (PWS) to explore the potential of this technology in engine applications. The PWS is a non-steady flow device that uses shock waves to pressurize fluids by transferring energy from a high-pressure flow to a low-pressure flow without separation by physical walls. The paper introduces a 1-D model of PWS in GT-SUITE calibrated by experiments on steady flow test rig. The 1-D model respects both exhaust and fresh air in each of the cells, friction and heat transfer in the cells as well as the continual opening and closing of the cells. Moreover, the cell wall temperature is computed and the leakage flow between the cells and housings modeled. The limits of PWS operation regarding pressures, temperatures and mass flows are first mapped on the virtual test rig utilizing the calibrated 1-D code based on the Mazda Comprex device. The device is further tested in GT-SUITE on a Yamaha YZF - R6 SI engine applied by CTU CarTech team as a powertrain in the Formula Student/SAE car. The engine full load, part load and transient response are simulated at different engine speeds and a possible PWS control technique introduced and evaluated by simulation. Further, the PWS control geometry is optimized to find the maximum boost pressure achievable and the optimized device simulated in conjunction with the Yamaha engine. Finally, a 0-D model suitable for prediction of engine response is presented. The 0-D model aims at a simple description of processes inside PWS based on physics and enables a close to real time simulation. The simplified processes are corrected by calibration coefficients determined by the 1-D model and transferred to the 0-D model through regression analysis. Comparison of developed 0-D and 1-D models at the engine transient operation is also provided and discussed.