Semi-analog monte carlo (SMC) method for time-dependent non-linear three-dimensional heterogeneous radiative transfer problems

Abstract

Radiative transfer is a complex phenomenon in which radiation field interacts with material. This thermal radiative transfer phenomenon is composed of two equations which are the balance equation of photons and the material energy balance equation. The two equations involve non-linearity due to the temperature and that makes the radiative transfer equation more difficult to solve. During the last several years, there have been many efforts to solve the non-linear radiative transfer problems by Monte Carlo method. Among them, it is known that Semi-Analog Monte Carlo (SMC) method developed by Ahrens and Larsen is accurate regard-less of the time step size in low temperature region. But their works are limited to one-dimensional, low temperature problems. In this thesis, we suggest some method to remove their limitations in the SMC method and apply to the more realistic problems. An initially cold problem was solved over entire temperature region by using piecewise linear interpolation of the heat capacity, while heat capacity is still fitted as a cubic curve within the lowest temperature region. If we assume the heat capacity to be linear in each temperature region, the non-linearity still remains in the radiative transfer equations. We then introduce the first-order Taylor expansion to linearize the non-linear radiative transfer equations. During the linearization procedure, absorption-reemission phenomena may be described by a conventional reemission time sampling scheme which is similar to the repetitive sampling scheme in particle transport Monte Carlo method. But this scheme causes significant stochastic errors, which necessitates many histories. Thus, we present a new reemission time sampling scheme which reduces stochastic errors by storing the information of absorption times. The results of the comparision of the two schemes show that the new scheme has less stochastic errors. Therefore, the improved SMC method is able to solve more realistic problems wit...