Reducing the Spatial Discretization Error of Thermal Emission in Implicit Monte Carlo Simulations

Irvine, Adam Glenn; Boyd, Iain D.; Gentile, N. A.

doi:10.1080/23324309.2015.1060245

Cited by 17 publications

(43 citation statements)

References 5 publications

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“…To be more precise, in this paper, we are even interested in being able to accurately capture a particular regime: in diffusive media, system (1) 4π dω = aT 4 m and Φ r (T r ) = aT 4 r , the second equation is equivalent to T m = T r : the radiative and matter temperatures are at equilibrium. In the above equation, δ ∼ 0 is a small parameter characterising what is commonly called the equilibrium 1 diffusion 2 limit [2,3,4]. The limit can be defined by introducing a characteristic length X , a characteristic time T and a characteristic collision rate λ and assuming we have…”

Section: Introductionmentioning

confidence: 99%

A new Implicit Monte-Carlo scheme for photonics (without teleportation error and without tilts)

Poëtte

Valentin

2020

Journal of Computational Physics

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In this paper, we present a new implicit Monte-Carlo scheme for photonics. The new solver combines the benefits of both the IMC solver of Fleck & Cummings and the SMC solver of Ahrens & Larsen. It is implicit hence allows taking affordable time steps (as IMC) and has no teleportation error (as SMC). The paper also provides some original analysis of existing schemes (IMC, tilted IMC, SMC), especially with respect to the teleportation error in the equilibrium diffusion regime. In particular, we demonstrate that any small spatial inaccuracies during the sampling of source particles for IMC lead to a competing behaviour between the spatial and time discretisation parameters. The new scheme we suggest is implicit, conservative, has no teleportation error (and as a consequence does not need tilting), does not rely on source sampling for the emission of source particles, captures the equilibrium diffusion limit (provided a small enough time step), can be used with arbitrary equations of state and does not suffer the above competing behaviour. All those properties are either demonstrated or numerically highlighted in the paper.

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Section: Introductionmentioning

confidence: 99%

A new Implicit Monte-Carlo scheme for photonics (without teleportation error and without tilts)

Poëtte

Valentin

2020

Journal of Computational Physics

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“…Using particle histories to aid in construction of the source tilts is seen to further mitigate teleportation error relative to standard linear tilts in T 4 . It seems, though, that using particle histories to construct the tilt may further couple MC noise into the simulation and may also be prohibitive with respect to memory (Irvine et al, 2011;Smedley-Stevenson and McClarren, 2015). With varying difficulty, these tilt schemes are extensible to multiple dimensions.…”

Section: Source Tilting Reviewmentioning

confidence: 96%

“…Consequently, for thermal waves, energy appears to "teleport" at non-physical speed to downstream cell locations (McKinley et al, 2003). Because it is often not computationally practical to introduce spatial grids that resolve mean-free-path length scales, effort has been made to mitigate teleportation error heuristically with material properties (i.e., temperature) (Fleck and Canfield, 1984;Cheatham, 2010;Irvine, Boyd, and Gentile, 2011;Urbatsch and Wollaber, 2011;Smedley-Stevenson and McClarren, 2015).…”

Section: Source Tilting Reviewmentioning

confidence: 98%

“…However, these schemes can lead to inconsistency between true cell average energy and average energy implied by the tilt profile. Irvine et al (2011) present a tilt scheme that uses particle paths and attenuation profiles along these paths to sample emission locations. Using particle histories to aid in construction of the source tilts is seen to further mitigate teleportation error relative to standard linear tilts in T 4 .…”

Section: Source Tilting Reviewmentioning

confidence: 99%

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Implicit Monte Carlo with a Linear Discontinuous Finite Element Material Solution and Piecewise Non-Constant Opacity

Wollaeger

Wollaber

Urbatsch

et al. 2016

Journal of Computational and Theoretical Transport

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KEYWORDSImplicit Monte Carlo (IMC); finite element; teleportation error; opacity ABSTRACTThe non-linear thermal radiative-transfer equations can be solved in various ways. One popular way is the Fleck and Cummings Implicit Monte Carlo (IMC) method. The IMC method was originally formulated with piecewise-constant material properties. For domains with a coarse spatial grid and large temperature gradients, an error known as numerical teleportation may cause artificially non-causal energy propagation and consequently an inaccurate material temperature. Source tilting is a technique to reduce teleportation error by constructing sub-spatial-cell (or sub-cell) emission profiles from which IMC particles are sampled. Several source tilting schemes exist, but some allow teleportation error to persist. We examine the effect of source tilting in problems with a temperature-dependent opacity. Within each cell, the opacity is evaluated continuously from a temperature profile implied by the source tilt. For IMC, this is a new approach to modeling the opacity. We find that applying both source tilting along with a source tilt-dependent opacity can introduce another dominant error that overly inhibits thermal wavefronts. We show that we can mitigate both teleportation and under-propagation errors if we discretize the temperature equation with a linear discontinuous (LD) trial space. Our method is for opacities ∼ 1/T 3 , but we formulate and test a slight extension for opacities ∼ 1/T 3.5 , where T is temperature. We find our method avoids errors that can be incurred by IMC with continuous source tilt constructions and piecewise-constant material temperature updates.

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“…To reduce teleportation error without relying on an interpolation of the temperature grid or functional form of the previous absorption locations, Irvine et al suggested storing particle absorption locations and ensuring that particles in the ensuing cycle sample their emission locations among the absorption locations from the previous cycle (Irvine, 2013;Irvine, Boyd, and Gentile, 2015). In the KULL ICF code (Rathkopf et al, 2000), Irvine reported enhanced accuracy for coarser spatial zoning at a relatively modest (25%) increase in memory usage for 3D problems and about a 13% decrease in compute time.…”

Section: Teleportation Errormentioning

confidence: 99%

Four Decades of Implicit Monte Carlo

Wollaber

2016

Journal of Computational and Theoretical Transport

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In 1971, Fleck and Cummings derived a system of equations to enable robust Monte Carlo simulations of time-dependent, thermal radiative transfer problems. Denoted the "Implicit Monte Carlo" (IMC) equations, their solution remains the de facto standard of high-fidelity radiative transfer simulations. Over the course of 44 years, their numerical properties have become better understood, and accuracy enhancements, novel acceleration methods, and variance reduction techniques have been suggested. In this review, we rederive the IMC equations-explicitly highlighting assumptions as they are made-and outfit the equations with a Monte Carlo interpretation. We put the IMC equations in context with other approximate forms of the radiative transfer equations and present a new demonstration of their equivalence to another well-used linearization solved with deterministic transport methods for frequency-independent problems. We discuss physical and numerical limitations of the IMC equations for asymptotically small time steps, stability characteristics and the potential of maximum principle violations for large time steps, and solution behaviors in an asymptotically thick diffusive limit. We provide a new stability analysis for opacities with general monomial dependence on temperature. We consider spatial accuracy limitations of the IMC equations and discussion acceleration and variance reduction techniques.

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Reducing the Spatial Discretization Error of Thermal Emission in Implicit Monte Carlo Simulations

Cited by 17 publications

References 5 publications

A new Implicit Monte-Carlo scheme for photonics (without teleportation error and without tilts)

A new Implicit Monte-Carlo scheme for photonics (without teleportation error and without tilts)

Implicit Monte Carlo with a Linear Discontinuous Finite Element Material Solution and Piecewise Non-Constant Opacity

Four Decades of Implicit Monte Carlo

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