Sadhana

, Volume 12, Issue 1–2, pp 105–123 | Cite as

Monte carlo simulation for molecular gas dynamics

  • S M Deshpande
  • PV Subba Raju
Aerodynamics

Abstract

The dynamics of low-density flows is governed by the Boltzmann equation of the kinetic theory of gases. This is a nonlinear integro-differential 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 particle-in-cell method and is based upon the Kac-Prigogine 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 Kac-Prigogine master equation collision dynamics Monte Carlo method unbiased and consistent estimator 

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Copyright information

© Indian Academy of Sciences 1988

Authors and Affiliations

  • S M Deshpande
    • 1
  • PV Subba Raju
    • 1
    • 2
  1. 1.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.Aerodynamics DivisionVikram Sarabhai Space CenterTrivandrumIndia

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