Symbolic implicit Monte Carlo radiation transport in the difference formulation: a piecewise constant discretization
type: Item
instance of: scholarly article
title: Symbolic implicit Monte Carlo radiation transport in the difference formulation: a piecewise constant discretization
zbMATH Open document ID: 1087.82004
author: Michael Scott McKinley
author: Frank Daffin
author: Eugene D. III. Brooks
author: Abraham Szőke
published in: Journal of Computational Physics
publication date: 2005-06-13T00:00:00Z
review text: The paper deals with equations of radiation transport for thermal photons. In particular, the slab geometry is considered. In this case the transport equation for the specific intensity \(I(x,t;\nu;\mu)\) reads \[ \frac{1}{c} \frac{\partial I}{\partial t} + \mu \frac{\partial I}{\partial x} = - \sigma'_{a}(\nu,T(x,t)) [I - B(\nu,T(x,t))] \;, \] where \(t\) is time, \(x\) is coordinate in the direction perpendicular to the slab, \(c\) is the speed of light, \(\nu\) is the radiation frequency, \(\mu = \cos \theta\), where \(\theta\) is the propogation angle, \(\sigma'_{a}\) is the absorption coefficient, and \(B(\nu,T(x,t))\) is the thermal (Planck) distribution at the material temperature \(T(x,t)\). The solution of such transport equations in thick media is a notoriously difficult problem. To overcome this difficulty, the authors use the difference formulation proposed in an earlier work. In this scheme, the transport equation is transformed by considering a new field \(D(x,t;\nu;\mu) = I(x,t;\nu;\mu) - B(\nu,T(x,t))\) that is the deviation of the local intensity from the local equilibrium intensity. It yields the transport equation \[ \frac{1}{c} \frac{\partial D}{\partial t} + \mu \frac{\partial D}{\partial x} = - \sigma'_{a} D - \frac{1}{c} \frac{\partial B}{\partial t} - \mu \frac{\partial B}{\partial x} \] for the new variable \(D\), which is solved by means of the symbolic implicit Monte Carlo method using a piecewise constant treatment of the material temperature. Several test problems are considered and comparisons are made between the standard formulation and the difference formulation. It is shown that the difference formulation leads to significant reduction of the noise and has a great computational advantage. The results also well agree with the analytical solution available for a linearised problem.
reviewed by: J. Kaupužs
Mathematics Subject Classification ID: 82-08
Mathematics Subject Classification ID: 82C70
Mathematics Subject Classification ID: 82C80
zbMATH DE Number: 2175591
zbMATH Keywords: radiation transport
zbMATH Keywords: difference formulation
zbMATH Keywords: implicit Monte Carlo
MaRDI profile type: Publication
full work available at URL: j.jcp.2004.11.026
OpenAlex ID: W2111435160
cites work: Q3796879
cites work: An implicit Monte Carlo scheme for calculating time and frequency dependent nonlinear radiation transport
cites work: Note on the Spherical Harmonic Method As Applied to the Milne Problem for a Sphere
cites work: Symbolic implicit Monte Carlo
cites work: Solution of the Nonlinear Radiative Transfer Equations by a Fully Implicit Matrix Monte Carlo Method Coupled with the Rosseland Diffusion Equation via Domain Decomposition
cites work: Asymptotic equilibrium diffusion analysis of time-dependent Monte Carlo methods for grey radiative transfer
cites work: Comparison of implicit and symbolic implicit Monte Carlo line transport with frequency weight vector extension
cites work: A random walk procedure for improving the computational efficiency of the implicit Monte Carlo method for nonlinear radiation transport
cites work: A linear-discontinuous spatial differencing scheme for \(S_ n\) radiative transfer calculations
cites work: Asymptotic analysis of a computational method for time- and frequency-dependent radiative transfer
cites work: Asymptotic diffusion limit of the symbolic Monte-Carlo method for the transport equation.
cites work: An evaluation of the difference formulation for photon transport in a two level system
cites work: Q3802475
DOI: 10.1016/J.JCP.2004.11.026
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description: scientific article; zbMATH DE number 2175591