A hybrid transport-diffusion method for Monte Carlo radiative-transfer simulations

Densmore, Jeffery D.; Urbatsch, Todd; Evans, Thomas M.; Buksas, M. W.

doi:10.1016/j.jcp.2006.07.031

Cited by 82 publications

(106 citation statements)

References 16 publications

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“…Discrete Diffusion Monte Carlo (DDMC) is another technique for increasing the efficiency of IMC in optically thick media [4,5]. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

Densmore

Thompson

Urbatsch

2012

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

Densmore

Thompson

Urbatsch

2012

Journal of Computational Physics

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“…Using a Monte Carlo method to solve the diffusion equation has the advantage that it is much easier to couple to the IMC method. Using the criteria def ned by Densmore et al, it is possible to transition particles from IMD (or DDMC) to IMC [11]. For the deterministic solution, the spatial domain must be decomposed and the deterministic solution could only be coupled to the IMC solution at the end of every time step.…”

Section: Discussionmentioning

confidence: 99%

“…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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“…We assume that the radiation at the base of the atmosphere is in thermal equilibrium with the material there. For this to be an accurate assumption, most photons emitted at the base of the atmosphere must be absorbed before they escape; this latter condition occurs when (Rybicki & , for greater accuracy; for Monte Carlo calculations, however, the computation time increases quadratically with total optical depth (Densmore et al 2007) and so we place the base right at this critical value. We have performed convergence studies in t base tot for a few cases and found differences of only a couple percent between the spectra in the t = 100 base tot case and the converged answer, and no detectable difference between the color correction factors for the two cases.…”

Section: Radiation-materials Interactionmentioning

confidence: 99%

Model Atmospheres for X-Ray Bursting Neutron Stars

Medin

Steinkirch

Calder

et al. 2016

ApJ

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The hydrogen and helium accreted by X-ray bursting neutron stars is periodically consumed in runaway thermonuclear reactions that cause the entire surface to glow brightly in X-rays for a few seconds. With models of the emission, the mass and radius of the neutron star can be inferred from the observations. By simultaneously probing neutron star masses and radii, X-ray bursts (XRBs) are one of the strongest diagnostics of the nature of matter at extremely high densities. Accurate determinations of these parameters are difficult, however, due to the highly non-ideal nature of the atmospheres where XRBs occur. Observations from X-ray telescopes such as RXTE and NuStar can potentially place strong constraints on nuclear matter once uncertainties in atmosphere models have been reduced. Here we discuss current progress on modeling atmospheres of X-ray bursting neutron stars and some of the challenges still to be overcome.

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A hybrid transport-diffusion method for Monte Carlo radiative-transfer simulations

Cited by 82 publications

References 16 publications

A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

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

Model Atmospheres for X-Ray Bursting Neutron Stars

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