Analysis of transport properties determined by Langevin dynamics using Green-Kubo formulae

Recently, the Langevin dynamics method has been applied to simulate gas flows. It is very crucial to evaluate whether the Langevin dynamics could correctly predict transport properties of gas or not. In this paper, the transport properties of Langevin velocity model and acceleration model are analyzed by using Green-Kubo formulae. For the Langevin velocity model, the time correlation functions have the exact exponent forms, and the Prandtl number for monatomic gas is predicted to be 3/2. For the Langevin acceleration model with an additional time scale, the molecular movements change from Markovian process to Non-Markovian process, and the Prandtl number could be adjusted to some extent. In the limit of equilibrium, there is a minimum about 1.298 for the Prandtl number of monatomic gas when the two time scales are equal in Langevin acceleration model. Besides theoretical analyses, molecular simulations according to the Langevin velocity model and acceleration model are performed, and the simulation results validate our analytical solutions.