Implicit Monte Carlo methods for coupled three-temperature transport

We present three methods for extending the Implicit Monte Carlo (IMC) method to treat the time-evolution of coupled radiation, electron, and ion energies. The first method splits the ion and electron coupling and conduction from the standard IMC radiation-transport process. The second method recasts the IMC equations such that part of the coupling is treated during the Monte Carlo calculation. The third method treats all of the coupling and conduction in the Monte Carlo simulation. Using Modified Equation Analysis (MEA), we show that the third method is theoretically the most accurate. We demonstrate the effectiveness of each method on a series of nonlinear benchmark problems where the accuracy of the third method is shown to be up to ten times greater than the other coupling methods for selected calculations. Also, the third method maintains first-order accuracy in time where the other methods lose first-order accuracy in thick problems.