Efficient numerical methods for solving the Boltzmann equation for small scale flows

The Navier-Stokes equations of continuum fluid mechanics fail to accurately describe dilute gas flows when the characteristic lengthscale of the system is on the order of (or smaller than) the molecular mean free path. At these lengthscales, gaseous hydrodynamics may be described by a kinetic description, namely the Boltzmann equation. Currently, the prevalent method for solving the Boltzmann equation is a particle simulation method known as direct simulation Monte Carlo (DSMC). DSMC is very efficient for high-speed (more generally, high signal) flows; unfortunately, due to the statistical sampling used to obtain hydrodynamic fields, the computational cost of DSMC (for a given signal to noise ratio) increases rapidly with decreasing signal. For example, the computational cost for calculating the flow velocity with a fixed signal to noise ratio scales with Ma-2 as Ma -- 0 (Ma is the Mach number). As a result, simulation of many low-signal flows of practical interest (for example, in micro- and nano-scale devices) is currently not feasible using DSMC. This thesis describes how the above limitation can be alleviated through the use of variance reduction techniques. In particular, we show that by simulating only the deviation from equilibrium, one can devise a variety of numerical methods that have a computational cost that is both small and independent of the magnitude of this deviation.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Baker, Lowell L. (Lowell Lane), 1980-

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/1721.1/39744

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/39744