Selection of sampling numerical parameters for the DSMC method

In this work the problem of selection of a number of numerical parameters of the direct simulation Monte Carlo (DSMC) method (such as time step, cell size, and number of time steps) is addressed. We study the errors of the DSMC method relating to the quality and amount of information sampled during simulation for three main macroparameters of a gas flow (density, velocity, and temperature). The expressions for optimal selection of the sampling time step, the number of sampling cells, 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. Practical recommendations are given for evaluating the quantities involved in the expressions simultaneously with the calculation of the flow macroparameters. The proposed approaches are examined on the examples of the Fourier problem, the gas recondensation problem between two infinite parallel plates, and the supersonic plane-parallel rarefied gas flow around a flat plate.

► We study errors of DSMC method relating to information sampled during simulation.
► We construct upper bound of sampling error for density, velocity, temperature.
► We propose expressions for optimal selection of the sampling numerical parameters.
► Proposed approaches are examined on examples of rarefied gas flows.