A Modified Symbolic Implicit Monte Carlo Method for Time-Dependent Thermal Radiation Transport

Symbolic Implicit Monte Carlo (SIMC) is fully implicit in the value of matter temperature used to calculate the thermal emission. However, it means that the temporal precision of this method is limited, despite this method being more robust than Fleck and Cummings' IMC method. In this article, we develop a new Monte Carlo method which is accurate for the thermal emission in one time step. Instead of solving a system of nonlinear equations as in SIMC, we rewrite the material energy balance equation as a system of ordinary differential equations by a waveform relaxation method. We find that the initial value problem associated with these ordinary differential equations has an analytical solution, meaning that we can convert the problem into solving a function of the material temperature at the end of a time step. We prove that the function is monotonic during a time step, so that a bisection method can be used to solve the equation. This calculation process avoids having to solve the matrix equations directly and instead they are converged by performing an outer iteration. Numerical experiments are performed to validate the accuracy and efficiency of the current approach.