Nonlinear radiation transport simulation with an implicit Monte Carlo method.

Milagro Version 2 An Implicit Monte Carlo Code for Thermal Radiative Transfer: Capabilities, Development, and Usage

“…Recent research has shown that the Carter and Forest method [35] might be a suitable replacement of Fleck and Cummings' IMC method [36].…”

A modified implicit Monte Carlo method for time-dependent radiative transfer with adaptive material coupling

“…The other main approximation in the Fleck and Cummings IMC method is that the instantaneous intensity, I, is used in the definition of u nþ1 r in going from Eqs. (7) to (8), which is equivalent to assuming that the time dependence of I does not influence the emission process. Under this assumption the re-emission process is instantaneous and is modeled by effective scattering.…”

“…Moreover, with the approximation that the time dependence of I does not affect the emission, the strength of the emission source cannot change over the time step. The Carter-Forest method [8] addresses this issue by defining timedependent source and re-emission terms that are sampled in the Monte Carlo solution of the transport equation. Also, other recent work has defined a time-dependent Fleck factor that tunes the parameter a to achieve a more accurate solution [11].…”

“…0021 Various methods have attempted to correct certain errors in the IMC method. The Carter-Forest method [8] exactly solves the linearized material energy equation through a Monte Carlo procedure and the symbolic implicit Monte Carlo (SIMC) method [9,10] does not have linearization error but does introduce a time discretization error. Other recent work has defined a time-dependent Fleck factor (and source term) to more accurately treat the time dependence of the intensity over a time step [11].…”

Accurate and Efficient Radiation Transport in Optically Thick Media – by Means of the Symbolic Implicit Monte Carlo Method in the Difference Formulation

“…The first one was overcome by the development of a Monte Carlo technique that is numerically stable and provides correct treatment of the stiff coupling between the radiation and the material in the thick limit. Several authors have shown that the radiation matter coupling is properly treated in the Symbolic Implicit Monte Carlo method [Bro86,Nka91], producing a correct implicit solution of the radiation field and the material temperature at the end of a time step [DL04], while effective scattering techniques [FC71,CF73] possess a significant deficiency in this regard.…”