Year: 2012
Author: Christopher R. Schrock, Aihua W. Wood
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 1 : pp. 102–121
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 $L^\infty$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.10-m11113
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 1 : pp. 102–121
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Direct simulation monte carlo rarefied gas dynamics Boltzmann equation convergence proof.
Author Details
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