The direct simulation Monte Carlo (DSMC) method is a stochastic approach to solve the Boltzmann equation and is built on various numerical schemes for transport, collision and sampling. This work aims to compare and contrast two popular O(N) DSMC collision schemes - no-time-counter (NTC) and majorant collision frequency (MCF) - with the goal of identifying the fundamental differences. MCF and NTC schemes are used in DSMC simulations of a spatially homogeneous equilibrium gas to study convergence with respect to various collision parameters. While the MCF scheme forces the reproduction of the exponential distribution of time between collisions, the NTC scheme requires larger number of simulators per cell to reproduce this Poisson process. The two collision schemes are also applied to the spatially homogeneous relaxation from an isotropic non-Maxwellian given by the Bobylev exact solution to the Boltzmann equation. While the two schemes produce identical results at large times, the initial relaxation shows some differences during the first few timesteps.


Copyright (2012) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in (A. Venkattraman*, A. A. Alexeenko, M. A. Gallis, and M. S. Ivanov, “A comparative study of no-time-counter and majorant collision frequency numerical schemes in DSMC”, Proceedings of 28th International Symposium on Rarefied Gas Dynamics, 9–13 July 2012, Zaragoza, Spain, AIP Conf. Proc. 1501, pp. 489-495.) and may be found at http://dx.doi.org/10.1063/1.4769577. The following article has been submitted to/accepted by [American Institute of Physics]. After it is published, it will be found at (http://dx.doi.org/10.1063/1.4769577). Copyright (2012) A. Venkattraman*, A. A. Alexeenko, M. A. Gallis, and M. S. Ivanov. This article is distributed under a Creative Commons Attribution 3.0 Unported License.

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