A fast simulation method with arbitrary viscosity law

Macrossan, M. N. (2005). A fast simulation method with arbitrary viscosity law. In: Mario Capitelli, Rarefied gas dynamics: 24th International Symposium on Rarefied Gas Dynamics. 24th International Symposium on Rarefied Gas Dynamics, Monopoli, Bari, Italy, (692-700). 10-16 July 2004. doi:10.1063/1.1941616

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Author Macrossan, M. N.
Title of paper A fast simulation method with arbitrary viscosity law
Conference name 24th International Symposium on Rarefied Gas Dynamics
Conference location Monopoli, Bari, Italy
Conference dates 10-16 July 2004
Proceedings title Rarefied gas dynamics: 24th International Symposium on Rarefied Gas Dynamics   Check publisher's open access policy
Journal name Rarefied Gas Dynamics   Check publisher's open access policy
Place of Publication New York, United States of America
Publisher American Institute of Physics
Publication Year 2005
Year available 2005
Sub-type Fully published paper
DOI 10.1063/1.1941616
ISBN 978-0-7354-0247-8
ISSN 0094-243X
Editor Mario Capitelli
Volume 762
Issue 1
Start page 692
End page 700
Total pages 9
Language eng
Abstract/Summary A new approach to DSMC collision modelling, called viscosity-DSMC or mu-DSMC, is described. The characteristic collision cross-section (of any standard collision model) is made to vary from cell to cell, based on the time-averaged temperature in each cell. In this way the collision model will display the Chapman-Enskog viscosity given by any desired viscosity law mu = mu(T), including a curve fit to experimental data. For example, we show that a hard sphere collision model, with hard sphere collision probability, used with a different molecular size in each cell, can reproduce a Sutherland viscosity law. Similarly, by making the reference cross-section of a VHS collision model a function of the temperature, we show that the VHS collision model can reproduce the viscosity given by the more complicated generalized hard sphere (GHS) collision model. We calculate the structure of a plane 1D shock using the new approach and show that the results agree closely with those from standard DSMC using the GHS model. A particularly simple, and computationally efficient, method is to use the Maxwell VHS model, in which all collision pairs are equally likely, as the basis of the new method. That is, the characteristic size of the maxwell VHS model is varied from cell to cell, based on the time-averaged cell temperature and the (arbitrary) desired viscosity law mu = mu(T). Since the time-averaged cell temperature is available in standard DSMC as part of the procedures which determine the steady state flow, the new methods are as fast as, or faster than DSMC using the standard VHS model. Unlike more complicated models with realistic viscosities, the new procedures are compatible with the Borgnakke-Larsen energy exchange scheme and the established chemistry models for DSMC. ©2005 American Institute of Physics
Subjects 240502 Fluid Physics
E1
Keyword DSMC
collision model
realistic viscosity
mu-DSMC
nu-DSMC
near-continuum
generalised hard sphere
GHS
References Kestin, J., Knierim, K., Mason, E. A., Najafi, B., Ro, S. T., and Waldman, M., J. Phys. Chem. Ref. Data , 13 , 229-303 (1984). Davis, J., Dominy, R. G., Harvey, J. K., and Macrossan, M. N., J. Fluid Mech. , 135 , 355-371 (1983). Sturtevant, B., and Steinhilper, E. A., Intermolecular potentials from shock structure experiments, in Rarefied Gas Dynamics. Proc. 8th Int. Symp. , edited by Karamcheti, Acadmeic Press, 1974, p. 159. Koura, K., and Matsumoto, H., Phys. Fluids A , 3 , 2459 - 2465 (1991). Erwin, D. A., Pham-Van-Diep, G. C., and Muntz, E. P., Phys. Fluids A, 3, 697 - 705 (1991). Hash, D. B., and Hassan, H. A., Phys. Fluids A, 5, 738 - 744 (1993). Koura, K., and Matsumoto, H., Phys. Fluids A, 4, 1083 - 1085 (1992). Borgnakke, C., and Larsen, P. S., J. Comput. Phys., 18, 405 (1975). Bird, G. A., J. Comput. Phys., 25, 353 (1977). Macrossan, M. N., J. Comput. Phys., 185, 612-627 (2003). Macrossan, M. N., J. Comput. Phys., 173, 600-619 (2001). Macrossan, M. N., and Lilley, C. R., J. Thermophys. Heat Trans., 17, 289-291 (2003). Erofeev, A. I., and Perepukhov, V. A., Hypersonic rarefied flow about a flat plate by the D irect S imulation M ethod, in Rarefied Gas Dynamics, edited by Camprague, C.E.A, Paris, France, 1979, p. 417. Bird, G. A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon, Oxford, 1994. Krook, M., and Wu, T. T., Phys. Fluids, 20, 1589 - 1595 (1977).
Q-Index Code E1
Additional Notes AIP Conference Proceedings Series, ISSN: 0094-243X, no. 762. For GHS model see Macrossan and Lilley, "Modified generalized hard sphere collision model for direct simulation Monte Carlo Calculations" J Thermo Phys Heat Trans 17 (2), 289-291 April (2003).

 
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Created: Fri, 25 Feb 2005, 10:00:00 EST by Michael N Macrossan on behalf of School of Engineering