|Student Name:||Christopher Schrock, civilian|
|Thesis:||Distributional Monte Carlo Methods for the Boltzmann Equation|
|Location:||Room 228 (Bldg 641)|
|Date & Time:||01/24/2013 at 1400|
|Abstract:|| 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. 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 presentation details the development of new SPMs that allow the velocity of each simulated particle to be distributed. These approaches have been termed Distributional Monte Carlo (DMC). The derivation of a general DMC framework is given which treats collision interactions between simulated particles as a relaxation problem. The framework is proven to converge in law to the solution of the space homogeneous Boltzmann equation, as well as in solution for L-infinity and bounded solutions. Each approach developed was applied to the Bobylev-Krook-Wu solution as a test case. Accuracy and variance of solutions are examined as functions of various simulation parameters, and significant improvement is observed for a DMC technique employing discrete collision modeling.