The Velocity Distribution Function in DSMC with an Application to Extended Thermodynamics

A numerical experiment is carried out to prove the difference between the value of the kinetic temperature and that of the thermodynamic temperature in a gas in the presence of molecular transport. As a reference situation the velocity distribution function is evaluated between two concentric cylinders at different wall temperatures. A direct simulation Monte Carlo method (DSMC) is adopted for various Knudsen numbers Kn and comparisons are made with existing data. The results prove quantitatively that the difference between the two differently defined temperatures increases with Kn and with the temperature gradient, as predicted by the theory for systems which are almost in thermodynamical equilibrium. The present article does not aim to validate DSMC, but rather to illustrate how the method can be used to address fundamental issues in gas dynamics.