Advanced Monte Carlo Methods for Thermal Radiation Transport.

During the past 35 years, the Implicit Monte Carlo (IMC) method proposed by Fleck and Cummings has been the standard Monte Carlo approach to solving the thermal radiative transfer (TRT) equations. However, the IMC equations are known to have accuracy limitations that can produce unphysical solutions. In this thesis, we explicitly provide the IMC equations with a Monte Carlo interpretation by including particle weight as one of its arguments. We also develop and test a stability theory for the 1-D, gray IMC equations applied to a nonlinear problem. We demonstrate that the worst case occurs for 0-D problems, and we extend the results to a stability algorithm that may be used for general linearizations of the TRT equations. We derive gray, Quasidiffusion equations that may be deterministically solved in conjunction with IMC to obtain an inexpensive, accurate estimate of the temperature at the end of the time step. We then define an average temperature $T_*$ to evaluate the temperature-dependent problem data in IMC, and we demonstrate that using $T_*$ is more accurate than using the (traditional) beginning-of-time-step temperature. We also propose an accuracy enhancement to the IMC equations: the use of a time-dependent ``Fleck factor''. This Fleck factor can be considered an automatic tuning of the traditionally defined user parameter $alpha$, which generally provides more accurate solutions at an increased cost relative to traditional IMC. We also introduce a global weight window that is proportional to the forward scalar intensity calculated by the Quasidiffusion method. This weight window improves the efficiency of the IMC calculation while conserving energy. All of the proposed enhancements are tested in 1-D gray and frequency-dependent problems. These enhancements do not unconditionally eliminate the unphysical behavior that can be seen in the IMC calculations. However, for fixed spatial and temporal grids, they suppress them and clearly work to make the solution more accurate. Overall, the work presented represents first steps along several paths that can be taken to improve the Monte Carlo simulations of TRT problems.Ph.D.Nuclear Engineering and Radiological Sciences and ScientifUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60735/1/wollaber_1.pd