Stochastic methods for modeling hydrodynamics of dilute gases

When modeling small scale sub-micron gas flows, continuum methods, i.e. Navier Stokes equations, no longer apply. Molecular Dynamics (MD) approaches are then more appropriate. For dilute gases, where particles travel in straight lines for the overwhelming majority of the time, MD methods are inefficient compared to kinetic theory approaches because they require the explicit calculation of each particle's trajectory. An effective way to model the hydrodynamics of dilute gases is a stochastic particle method known as Direct Simulation Monte Carlo (DSMC). In DSMC the motion and collision of particles are decoupled to increase computational efficiency. The purpose of this thesis is to evaluate a variant of the DSMC algorithm, in which particles have discrete velocities. The most important modification to the DSMC algorithm is the treatment of collisions between particles with discrete velocities in a way which ensures strict conservation of momentum and energy. To achieve that an algorithm that finds all possible pairs of discrete post-collision velocities given a pair of discrete pre-collision velocities was developed and coded.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Hayeck, Tristan J

Advisor dc:contributor.advisor

• Nicolas 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/1721.1/36745

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/36745