Abstract
The formation of shock and expansion waves by a moving piston is studied according to the kinetic theory of gases. A piston is impulsively moved at a constant but arbitrary speed with a diffuse reflection on either isothermal or adiabatic piston wall. The Bhatnagar-Gross-Krook equation has been solved by applying the numerical method proposed by Chu for the shock tube problem. The waves are developed through intermolecular collisions for various piston speeds (Mach number 0.438, 0.876, and 1.314). The properties across the shock wave agree quite well with the Rankine-Hugoniot relations. A kinetic layer of several mean free paths near the isothermal piston wall is clearly observed. A temperature jump at the isothermal wall is also developed. Solutions for the adiabatic wall with zero temperature gradient are obtained and compared very well with the gas dynamic solutions. Temperature overshoots (Tx) inside the shock waves have been observed for higher piston speeds (Mach number 0.876 and 1.314).
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