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

Published online by Cambridge University Press:  20 August 2015

Jonathan M. Burt  and
Iain D. Boyd
Jonathan M. Burt*
Affiliation:
U.S. Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA
Iain D. Boyd*
Affiliation:
Department of Aerospace Engineering, University of Michigan, 1320 Beal Avenue, Ann Arbor, MI 48109, USA
*
Corresponding author.Email:jonathan.m.burt@nasa.gov
Email:iainboyd@umich.edu
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Abstract

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.

Keywords

65C0576M28Monte Carlo methodsparticle methodsdirect simulation Monte Carlo
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 4 , October 2011 , pp. 807 - 822
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Bird, G. A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford, 1994.Google Scholar
[2]Boyd, I. D., Direct Simulation Monte Carlo for Atmospheric Entry Part I: Theoretical Basis and Physical Models, Hypersonic Entry and Cruis Vehicles, von Karman Institute for Fluid Dynamics, Rhode-Saint-Genese, Belgium, 2008.Google Scholar
[3]Rieffel, M. A., A method for estimating the computational requirements of DSMC simulations, J. Comput. Phys., 149 (1999), 95–113.Google Scholar
[4]Bird, G. A., The DS2V/3V program suite for DSMC calculations, rarefied gas dynamics: 24th International Symposium, American Institute of Physics, 2005, 541–546.Google Scholar
[5]Rault, D. F. G., Aerodynamic characteristics of a hypersonic viscous optimized waverider at high altitudes, AIAA Paper, (1992), 92–0306.Google Scholar
[6]Skellam, J. G., The frequency distribution of the difference between two Poisson variates belonging to different populations, J. Roy. Statist. Soc., 109 (1946), 296.Google Scholar
[7]Hadjiconstantinou, N. G., Garcia, A. L., Bazant, M. Z. and He, G., Statistical error in particle simulations of hydrodynamic phenomena, J. Comput. Phys., 187 (2003), 274–297.Google Scholar
[8]Dietrich, S. and Boyd, I. D., Scalar and parallel optimized implementation of the direct simulation Monte Carlo method, J. Comput. Phys., 126 (1996), 328–342.Google Scholar
[9]Boyd, I. D., Analysisof rotational nonequilibrium in standing shock wavesof nitrogen, AIAA J., 28 (1990), 1997–1999.Google Scholar