## Discrete Diffusion Monte Carlo for grey Implicit Monte Carlo simulations.

Discrete Diffusion Monte Carlo (DDMC) is a hybrid transport-diffusion method for Monte Carlo simulations in diffusive media. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Thus, DDMC produces accurate solutions while increasing the efficiency of the Monte Carlo calculation. In this paper, we extend previously developed DDMC techniques in several ways that improve the accuracy and utility of DDMC for grey Implicit Monte Carlo calculations. First, we employ a diffusion equation that is discretized in space but is continuous time. Not only is this methodology theoretically more accurate than temporally discretized DDMC techniques,more »