Investigation of monte carlo methods for time-dependent nonlinear radiative transfer problems

Abstract

Radiative transfer is complex algebraically but has a simple physics content. It only states energy conservation`s law between radiation energy and material balance energy. But radiative transfer equation has temperature as parameter, which makes the radiative transfer equation nonlinear. The nonlinearity makes the radiative transfer equation difficult to be treated. This complicated time-dependent nonlinear radiative transfer equation can be solved by Monte Carlo Method. Implicit Monte Carlo method (IMC) has described it for a long time until now. But new Monte Carlo method is being studied because IMC has a difficulty about time step. That is,IMC is very accurate in small time step but is not accurate in large time step. Semi-analog Monte Carlo (SMC), one of Monte Carlo methods which were developed recently, is very accurate regardless of time step. In this study, radiative transfer treated is grey radiative transfer which is independent of frequency. Two Monte Carlo methods are used. One is IMC method developed by Fleck, Jr and Cummings, the other is SMC method developed by Ahrehs and Larsen. They are applied to solve grey linear radiative transfer problem and then compared. Physical properties were constants to be solved it simply. Especially specific heat is used Debye`s one which is well described at all temperature, An approximation of low temperature of it is used, and then the equation becomes linear without temperature term. We solve radiative transfer problems which have analytic solution and do not have analytic solution. In addition, parallel computing is implemented. Variance is analyzed about total temporal and spatial distribution. We study how Monte Carlo particles are born to obtain a desired temporal and spatial tally, especially to reduce variance about a difficult region, and apply it to reduce the variance.