Abstract
A new scheme, the modified direct simulation Monte-Carlo (MDSMC), for the numerical simulation of the Boltzmann equation for rarefied gas flow about a sphere is developed. The Taylor series expansion is used to obtain the modified equation of the first-order time discretization of the collision equation and the new scheme, MDSMC, is implemented to simulate the collision equation in the Boltzmann equation. In the new scheme (MDSMC) there exists a new extra term which takes into account the effect of the second-order collision. In the new scheme (MDSMC) there also exists a second-order term in time step in the probabilistic coefficients which has the effect of simulation with higher accuracy than the previous DSMC scheme. The results of the drag coefficient of the sphere using the MDSMC scheme show better agreement in comparison with the experimental data of Wegener (1961) than the results of the drag coefficient of the sphere using the DSMC scheme.
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This paper was recommended for publication in revised form by Associate Editor Man-Yeong Ha
S. S. Nourazar received his B.Sc. degree from Amirkabir University of Technology in Tehran, Iran. Then he continued his graduate studies in Canada and received the M. Sc. and Ph.D in Mechanical engineering from Ottawa University in Canada. Dr. Nourazar is acting now as associate professor in the Mechanical Engineering Department of Amirkabir University of Technology. His research interests are the CFD in compressible and incompressible turbulent nonreactive flow as well as rarefied gas dynamics.
A. A. Ganjaei received his B.Sc. degree from Science & Technology of Iran University in Tehran, Iran. Then he continued his graduate studies in Amirkabir University of Technology and received the M. Sc. and PhD in Mechanical engineering. The research interests of Ganjaei are the CFD in compressible and incompressible turbulent nonreactive flow as well as rarefied gas dynamics.
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Nourazar, S.S., Ganjaei, A.A. A new scheme developed for the numerical simulation of the Boltzmann equation using the direct simulation monte-carlo scheme for the flow about a sphere. J Mech Sci Technol 24, 1989–1996 (2010). https://doi.org/10.1007/s12206-010-0715-7
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DOI: https://doi.org/10.1007/s12206-010-0715-7