Date of Award
Doctor of Philosophy (PhD)
Department of Mathematics and Statistics
Aihua W. Wood, PhD.
Stochastic particle methods (SPMs) for the Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) technique, have gained popularity for the prediction of flows in which the assumptions behind the continuum equations of fluid mechanics break down; however, there are still a number of issues that make SPMs computationally challenging for practical use. In traditional SPMs, simulated particles may possess only a single velocity vector, even though they may represent an extremely large collection of actual particles. This limits the method to converge only in law to the Boltzmann solution. This document details the development of new SPMs that allow the velocity of each simulated particle to be distributed. This approach has been termed Distributional Monte Carlo (DMC).
DTIC Accession Number
Schrock, Christopher R., "Distributional Monte Carlo Methods for the Boltzmann Equation" (2013). Theses and Dissertations. 958.