MONTE CARLO METHOD FOR SIMULATING IDEAL GAS RATE DISTRIBUTION AND ITS APPLICATION

The Maxwell-Boltzmann distribution is a very important form of distribution corresponding to classical particles in statistical mechanics. Ideal gases, as representatives of classical particles, provide the basis for studying distribution mentioned above. However, most of the studies only prove the rationality of the Maxwell-Boltzmann distribution, seldom study the evolution of classical ideal gases to thermal equilibrium, and fail to integrate the evolution process with practical applications. Therefore, based on the elastic collision in center of mass system, this article aims to use to simulate the process for ideal gas reaching equilibrium with the Monte Carlo method. An error function is proposed to quantify the error between ideal gas and simulated gas, and investigating the variation of the error with the quantity of the simulated particles and the number of collisions in the simulation process. The convergence rate of different velocity initialization methods is discussed, and a scheme for high precision simulation with small computational cost is given. Finally, the methods are applied to the simulation of single-particle Brownian motion and the simulation on effusion of gas through a small hole, the results are consistent with the theory.