Symbolic implicit Monte Carlo radiation transport in the difference formulation: a piecewise constant discretization

Brooks, Eugene D.; McKinley, Michael Scott; Daffin, F.; Szöke, A.

doi:10.1016/j.jcp.2004.11.026

Cited by 11 publications

(30 citation statements)

References 20 publications

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“…The difference formulation is a variance reduction technique which changes the source of the problem to focus the computational work where the solution is rapidly changing [9]. We def ne a new quantity, e d [ν], which is the difference between the radiation energy density and the Planckian def ned at some user-specif ed temperature T d ,…”

Section: The Difference Formulationmentioning

confidence: 99%

“…If an emission source term is approximated as piecewise constant in a spatial cell, and the actual source distribution has a strong dependence on space in the cell, particles will artif cially be redistributed (or teleported) from regions where the source is large to regions where it is small. This discretization artifact is known as teleportation error [9]. The original form of SIMC which relies on piecewise constant basis functions does not approach the diffusion limit and suffers from teleportation error problems [9].…”

Section: Introductionmentioning

confidence: 99%

“…This discretization artifact is known as teleportation error [9]. The original form of SIMC which relies on piecewise constant basis functions does not approach the diffusion limit and suffers from teleportation error problems [9]. A piecewise linear SIMC was shown to approach the diffusion limit and is much less affected by teleportation error [8,20].…”

Section: Introductionmentioning

confidence: 99%

“…More recent research has extended SIMC to include frequency dependence in the hybrid diffusion transport method. The difference formulation, discussed in detail below, for SIMC was also developed and has been shown to reduce variance in thick problems [9].…”

Section: Introductionmentioning

confidence: 99%

“…If the reference Planckian is set equal to the Planckian of the current material state, computational cost is shifted to regions where the material and photon energy densities are out of equilibrium. The difference formulation has been explored primarily in SIMC and has been shown to signif cantly increase the f gure of merit compared to the standard solution [13,9]. It has also been shown to yield promising results when used with IMC [14], but has not been explored in conjunction with Implicit Monte Carlo Diffusion (IMD) [1] or Discrete Diffusion Monte Carlo (DDMC) [11].…”

Section: Introductionmentioning

confidence: 99%

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An extension of implicit Monte Carlo diffusion: Multigroup and the difference formulation

Cleveland

Gentile

Palmer

2010

Journal of Computational Physics

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Implicit Monte Carlo (IMC) and Implicit Monte Carlo Diffusion (IMD) are approaches to the numerical solution of the equations of radiative transfer. IMD was previously derived and numerically tested on grey, or frequency-integrated problems [1]. In this research, we extend Implicit Monte Carlo Diffusion (IMD) to account for frequency dependence, and we implement the difference formulation [2] as a source manipulation variance reduction technique. We derive the relevant probability distributions and present the frequency dependent IMD algorithm, with and without the difference formulation. The IMD code with and without the difference formulation was tested using both grey and frequency dependent benchmark problems. The Su and Olson semi-analytic Marshak wave benchmark was used to demonstrate the validity of the code for grey problems [3]. The Su and Olson semi-analytic picket fence benchmark was used for the frequency dependent problems [4]. The frequency dependent IMD algorithm reproduces the results of both Su and Olson benchmark problems. Frequency group ref nement studies indicate that the computational cost of ref ning the group structure is likely less than that of group ref nement in deterministic solutions of the radiation diffusion methods. Our results show that applying the difference formulation to the IMD algorithm can result in an overall increase in the f gure of merit for frequency dependent problems. However, the creation of negatively weighted particles from the difference formulation can cause signif cant numerical instabilities in regions of the problem with sharp spatial gradients in the solution. An adaptive implementation of the difference formulation may be necessary to focus its use in regions that are at or near thermal equilibrium.

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Section: The Difference Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An extension of implicit Monte Carlo diffusion: Multigroup and the difference formulation

Cleveland

Gentile

Palmer

2010

Journal of Computational Physics

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

Szöke

Brooks

McKinley

et al.

Lecture Notes in Computational Science and Engineering

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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.

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Monte Carlo radiative transfer

Noebauer

Sim

2019

Living Rev Comput Astrophys

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The theory and numerical modelling of radiation processes and radiative transfer play a key role in astrophysics: they provide the link between the physical properties of an object and the radiation it emits. In the modern era of increasingly high-quality observational data and sophisticated physical theories, development and exploitation of a variety of approaches to the modelling of radiative transfer is needed. In this article, we focus on one remarkably versatile approach: Monte Carlo Radiative Transfer (MCRT). We describe the principles behind this approach, and highlight the relative ease with which they can (and have) been implemented for application to a range of astrophysical problems. All MCRT methods have in common a need to consider the adverse consequences of Monte Carlo (MC) noise in simulation results. We overview a range of methods used to suppress this noise and comment on their relative merits for a variety of applications. We conclude with a brief review of specific applications for which MCRT methods are currently popular and comment on the prospects for future developments.

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Symbolic implicit Monte Carlo radiation transport in the difference formulation: a piecewise constant discretization

Cited by 11 publications

References 20 publications

An extension of implicit Monte Carlo diffusion: Multigroup and the difference formulation

An extension of implicit Monte Carlo diffusion: Multigroup and the difference formulation

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

Monte Carlo radiative transfer

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