Estimation of the statistical error and the choice of parameters in the method of test particles

The method of test particles is considered for the solution of the linearized Boltzmann equation using two types of stochastic estimators: with respect to time and to intersections. Based on these estimators, functional algorithms for the approximation of three macroparameters of test particle flows (density, velocity, and temperature) are constructed in the whole domain. A new approach to the construction of confidence intervals determining statistical errors of the velocity and temperature estimates is proposed. Upper bounds for errors of functional algorithms approximating the macroparameters of the flow in the metric of the space of continuous functions are constructed. Based on these bounds, the optimal sample amount and the number of grid nodes are obtained to guarantee that the calculation error for each macroparameter does not exceed a given level with a given probability. The optimal values obtained here are tested numerically on the example of the classic problem of heat transfer between two parallel plates.