Commun. Comput. Phys., 10 (2011), pp. 807-822.

Convergence Detection in Direct Simulation Monte Carlo Calculations for Steady State Flows

Jonathan M. Burt 1*, Iain D. Boyd 2

1 U.S. Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA.
2 Department of Aerospace Engineering, University of Michigan, 1320 Beal Avenue, Ann Arbor, MI 48109, USA.

Received 9 February 2010; Accepted (in revised version) 31 December 2010
Available online 13 June 2011


A new criterion is presented to detect global convergence to steady state, and to identify local transient characteristics, during rarefied gas flow simulations performed using the direct simulation Monte Carlo (DSMC) method. Unlike deterministic computational fluid dynamics (CFD) schemes, DSMC is generally subject to large statistical scatter in instantaneous flow property evaluations, which prevents the use of residual tracking procedures as are often employed in CFD simulations. However, reliable prediction of the time to reach steady state is necessary for initialization of DSMC sampling operations. Techniques currently used in DSMC to identify steady state convergence are usually insensitive to weak transient behavior in small regions of relatively low density or recirculating flow. The proposed convergence criterion is developed with the goal of properly identifying such weak transient behavior, while adding negligible computational expense and allowing simple implementation in any existing DSMC code. Benefits of the proposed technique over existing convergence detection methods are demonstrated for representative nozzle/plume expansion flow, hypersonic blunt body flow and driven cavity flow problems.

AMS subject classifications: 65C05, 76M28

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Key words: Monte Carlo methods, particle methods, direct simulation Monte Carlo.

*Corresponding author.
Email: (J. M. Burt), (I. D. Boyd)

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