, Volume 12, Issue 1, pp 105123
First online:
Monte carlo simulation for molecular gas dynamics
 S M DeshpandeAffiliated withDepartment of Aerospace Engineering, Indian Institute of Science
 , PV Subba RajuAffiliated withDepartment of Aerospace Engineering, Indian Institute of ScienceAerodynamics Division, Vikram Sarabhai Space Center
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The dynamics of lowdensity flows is governed by the Boltzmann equation of the kinetic theory of gases. This is a nonlinear integrodifferential equation and, in general, numerical methods must be used to obtain its solution. The present paper, after a brief review of Direct Simulation Monte Carlo (DSMC) methods due to Bird, and Belotserkovskii and Yanitskii, studies the details of theDSMC method of Deshpande for mono as well as multicomponent gases. The present method is a statistical particleincell method and is based upon the KacPrigogine master equation which reduces to the Boltzmann equation under the hypothesis of molecular chaos. The proposed Markoff model simulating the collisions uses a Poisson distribution for the number of collisions allowed in cells into which the physical space is divided. The model is then extended to a binary mixture of gases and it is shown that it is necessary to perform the collisions in a certain sequence to obtain unbiased simulation.
Keywords
Low density flow Boltzmann equation KacPrigogine master equation collision dynamics Monte Carlo method unbiased and consistent estimator Title
 Monte carlo simulation for molecular gas dynamics
 Journal

Sadhana
Volume 12, Issue 12 , pp 105123
 Cover Date
 198802
 DOI
 10.1007/BF02745661
 Print ISSN
 02562499
 Online ISSN
 09737677
 Publisher
 Springer India
 Additional Links
 Topics
 Keywords

 Low density flow
 Boltzmann equation
 KacPrigogine master equation
 collision dynamics
 Monte Carlo method
 unbiased and consistent estimator
 Industry Sectors
 Authors

 S M Deshpande ^{(1)}
 PV Subba Raju ^{(1)} ^{(2)}
 Author Affiliations

 1. Department of Aerospace Engineering, Indian Institute of Science, 560 012, Bangalore, India
 2. Aerodynamics Division, Vikram Sarabhai Space Center, 695 022, Trivandrum, India