Weighted particle variance reduction of Direct Simulation Monte Carlo for the Bhatnagar-Gross-Krook collision operator

Direct Simulation Monte Carlo (DSMC)-the prevalent stochastic particle method for high-speed rarefied gas flows-simulates the Boltzmann equation using distributions of representative particles. Although very efficient in producing samples of the distribution function, the slow convergence associated with statistical sampling makes DSMC simulation of low-signal situations problematic. In this thesis, we present a control-variate-based approach to obtain a variance-reduced DSMC method that dramatically enhances statistical convergence for lowsignal problems. Here we focus on the Bhatnagar-Gross-Krook (BGK) approximation, which as we show, exhibits special stability properties. The BGK collision operator, an approximation common in a variety of fields involving particle mediated transport, drives the system towards a local equilibrium at a prescribed relaxation rate. Variance reduction is achieved by formulating desired (non-equilibrium) simulation results in terms of the difference between a non-equilibrium and a correlated equilibrium simulation. Subtracting the two simulations results in substantial variance reduction, because the two simulations are correlated. Correlation is achieved using likelihood weights which relate the relative probability of occurrence of an equilibrium particle compared to a non-equilibrium particle. The BGK collision operator lends itself naturally to the development of unbiased, stable weight evaluation rules. Our variance-reduced solutions are compared with good agreement to simple analytical solutions, and to solutions obtained using a variance-reduced BGK based particle method that does not resemble DSMC as strongly. A number of algorithmic options are explored and our final simulation method, (VR)2-BGK-DSMC, emerges as a simple and stable version of DSMC that can efficiently resolve arbitrarily low-signal flows.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2010

Author dc:creator

• Landon, Colin Donald

Advisor dc:contributor.advisor

• Nicolas G. Hadjiconstantinou.

• Mechanical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/61882

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/61882