Frequency-Dependent Discrete Implicit Monte Carlo Scheme for the Radiative Transfer Equation

This work generalizes the discrete implicit Monte Carlo (DIMC) method for modeling the radiative transfer equation from a gray treatment to a frequency-dependent one. The classic implicit Monte Carlo (IMC) algorithm, which has been used for several decades, suffers from a well-known numerical problem, called teleportation, where the photons might propagate faster than the exact solution due to the finite size of the spatial and temporal resolution. The semi-analog Monte Carlo algorithm proposed the use of two kinds of particles, photons and material particles, that are born when a photon is absorbed. The material particle can “propagate” only by transforming into a photon due to black-body emissions. While this algorithm produces a teleportation-free result, its results are noisier compared to the IMC due to the discrete nature of the absorption-emission process. In a previous work, Steinberg and Heizler [ApJS, Vol. 258, p. 14 (2022)] proposed a gray version of DIMC that makes use of two kinds of particles, and therefore has teleportation-free results, but also uses the continuous absorption algorithm of IMC, yielding smoother results. This work is a direct frequency-dependent (energy-dependent) generalization of the DIMC algorithm. We find in several one- and two-dimensional benchmarks that the new frequency-dependent DIMC algorithm yields teleportation-free results on one hand, and smooth results with an IMC-like noise level.