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

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dc.contributor.advisor Nicolas G. Hadjiconstantinou. en_US Landon, Colin Donald en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mechanical Engineering. en_US 2011-03-24T20:21:05Z 2011-03-24T20:21:05Z 2010 en_US 2010 en_US
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010. en_US
dc.description Cataloged from PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 67-69). en_US
dc.description.abstract 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. en_US
dc.description.statementofresponsibility by Colin Donald Landon. en_US
dc.format.extent 69 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
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. en_US
dc.rights.uri en_US
dc.subject Mechanical Engineering. en_US
dc.title Weighted particle variance reduction of Direct Simulation Monte Carlo for the Bhatnagar-Gross-Krook collision operator en_US
dc.title.alternative Weighted particle variance reduction of DSMC for the BGK collision operator en_US
dc.type Thesis en_US S.M. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mechanical Engineering. en_US
dc.identifier.oclc 706147370 en_US

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