0

Full Content is available to subscribers

Subscribe/Learn More  >

A Variance Reduction Approach for Monte Carlo Solutions of the Non-Linear Boltzmann Equation

[+] Author Affiliations
Lowell L. Baker, Nicolas G. Hadjiconstantinou

Massachusetts Institute of Technology, Cambridge, MA

Paper No. ICMM2005-75099, pp. 453-460; 8 pages
doi:10.1115/ICMM2005-75099
From:
  • ASME 3rd International Conference on Microchannels and Minichannels
  • ASME 3rd International Conference on Microchannels and Minichannels, Parts A and B
  • Toronto, Ontario, Canada, June 13–15, 2005
  • Conference Sponsors: Nanotechnology Institute
  • ISBN: 0-7918-4185-5 | eISBN: 0-7918-3758-0
  • Copyright © 2005 by ASME

abstract

We show that simple and efficient Monte Carlo-based solution methods for the Boltzmann equation for low-speed applications can be constructed by using appropriate variance reduction techniques. More specifically, we show that evaluation of the collision integral by sampling a representative number of collisions can be significantly accelerated by considering only the deviation from equilibrium, since this allows one to avoid considering a large number of collisions with no net effect. As the deviation from equilibrium decreases, the degree of variance reduction increases, leading to a signal to noise ratio that remains approximately constant. Thus, unlike particle techniques in which statistical sampling results in computational cost that is inversely proportional to the square of the Mach number, the approach presented here exhibits computational cost which is almost independent of the Mach number in the small Mach number limit. This is verified by numerical experiments at Mach numbers as low as O(10−5 ). We validate this approach by comparing its results with analytical and direct Monte Carlo simulations of the Boltzmann equation.

Copyright © 2005 by ASME
Topics: Equations

Figures

Tables

Interactive Graphics

Video

Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature

Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

NOTE:
Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In