Statistical Error and Optimal Parameters of the Test Particle Monte Carlo Method

摘要

The test particle Monte Carlo method for solving the linearized Boltzmann equation is considered. This method is used for simulation of a gas mixture flow when the concentration of one of the component is low. We study the errors of the method for three main macroparameters (density, velocity, and temperature). The new approach to construction of asymptotic confidence intervals for the estimates of velocity and temperature is proposed. The expressions for optimal selection of the number of grid nodes and the sample size which guarantee attaining a specified level of the error are proposed on the basis of the theory of functional Monte Carlo algorithms. The proposed approaches are examined on the examples of the classical problem of heat transfer between two parallel plates and the two-dimensional problem of a transversal supersonic flow of a rarefied binary gas mixture around a plate.