Convergence of A Distributional Monte Carlo Method for the Boltzmann Equation

Document Type

Article

Publication Date

2-2012

Abstract

Direct Simulation Monte Carlo (DSMC) methods for the Boltzmann equation employ a point measure approximation to the distribution function, as simulated particles may possess only a single velocity. This representation limits the method to converge only weakly to the solution of the Boltzmann equation. Utilizing kernel density estimation we have developed a stochastic Boltzmann solver which possesses strong convergence for bounded and L ∞ solutions of the Boltzmann equation. This is facilitated by distributing the velocity of each simulated particle instead of using the point measure approximation inherent to DSMC. We propose that the development of a distributional method which incorporates distributed velocities in collision selection and modeling should improve convergence and potentially result in a substantial reduction of the variance in comparison to DSMC methods. Toward this end, we also report initial findings of modeling collisions distributionally using the Bhatnagar-Gross-Krook collision operator.

Comments

Copyright © Global-Science Press 2012

Co-author C. Schrock was an AFIT PhD student at the time of this publication. (AFIT-ENC-DS-13-M-06, March 2013)

Source Publication

Advances in Applied Mathematics and Mechanics (ISSN 2070-0733)

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