Abstract
We present a new algorithm for radiative transfer, based on a statistical
Monte-Carlo approach, that does not suffer from teleportation effects on the
one hand, and yields smooth results on the other hand. Implicit-Monte-Carlo
(IMC) techniques for modeling radiative transfer exist from the 70's. However,
in optically thick problems, the basic algorithm suffers from `teleportation'
errors, where the photons propagate faster than the exact physical behavior,
due to the absorption-black body emission processes. One possible solution is
to use semi-analog Monte-Carlo, in its new implicit form (ISMC), that uses two
kinds of particles, photons and discrete material particles. This algorithm
yields excellent teleportation-free results, however, it also results with
nosier solutions (relative to classic IMC) due to its discrete nature. Here, we
derive a new Monte-Carlo algorithm, Discrete implicit Monte-Carlo (DIMC) that
uses the idea of the two-kind discrete particles and thus, does not suffer from
teleportation errors. DIMC implements the IMC discretization and creates new
radiation photons each time step, unlike ISMC. This yields smooth results as
classic IMC, due to the continuous absorption technique. One of the main parts
of the algorithm is the avoidance of population explosion of particles, using
particle merging. We test the new algorithm in both one and two-dimensional
cylindrical problems, and show that it yields smooth, teleportation-free
results. We finish in demonstrating the power of the new algorithm in a classic
radiative hydrodynamic problem, an opaque radiative shock wave. This
demonstrates the power of the new algorithm in astrophysical scenarios.
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