Kinetic theory of piston problem and thermal disturbance by the ellipsoidal statistical model

The formation of shock waves by a moving piston and the thermal disturbance of a fixed wall by sudden temperature change are studied according to the kinetic theory of gases. The ellipsoidal statistical model which gives the correct Prandtl number for a monatomic gas is solved numerically. The perturbation method proposed by Chu is applied. Velocity, density, temperature, and pressure distributions are calculated at each time step for various piston speeds for the piston problem. A comparison between the Bhatnager-Gross-Krook model solution and the ellipsoidal statistical model solution is made. The thermal disturbances of velocity, density, and temperature are calculated at each time step for various wall temperatures. A comparison between the Kovitz-Hellman solutions and the ellipsoidal model is made.