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

Abstract

The equations of radiation transport for thermal photons are notoriously difficult to solve in thick media without resorting to asymptotic approximations such as the diffusion limit. One source of this difficulty is that in thick, absorbing media thermal emission is almost completely balanced by strong absorption. In a previous publication [SB03], the photon transport equation was written in terms of the deviation of the specific intensity from the local equilibrium field. We called the new form of the equations the difference formulation. The difference formulation is rigorously equivalent to the original transport equation. It is particularly advantageous in thick media, where the radiation field approaches local equilibrium and the deviations from the Planck distribution are small. The difference formulation for photon transport also clarifies the diffusion limit. In this paper, the transport equation is solved by the Symbolic Implicit Monte Carlo (SIMC) method and a comparison is made between the standard formulation and the difference formulation. The SIMC method is easily adapted to the derivative source terms of the difference formulation, and a remarkable reduction in noise is obtained when the difference formulation is applied to problems involving thick media.

General relativistic radiation hydrodynamics of accretion flows - I. Bondi-Hoyle accretion

“…Since the dynamics of V09.CS07 becomes radiation pressure dominated around t ∼ 5000 M, the explanation of this effect is simple: in such conditions the effective adiabatic index of the fluid-plus-radiation medium is smaller than that of the fluid alone [see equation 70.22 of Mihalas & Mihalas (1999)] 5 We recall that the relativistic Mach number is defined as M = v/(c s s ), where and s are the Lorentz factors of the flow and of the sound speed, respectively. 6 The present version of the code does not allow us to handle stiff source terms that arise in the radiation-hydrodynamic equations when the conductivity is small (Szőke et al 2006). Work is in progress to cope with this difficulty.…”

“…6 6 The present version of the code does not allow us to handle stiff source terms that arise in the radiation‐hydrodynamic equations when the conductivity is small (Szőke et al 2006). Work is in progress to cope with this difficulty. …”