Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity

Wollaeger, Ryan T.; Wollaber, Allan B.; Urbatsch, Todd J.; Densmore, Jeffery D.

doi:10.1080/23324309.2016.1157491

Title: Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity

Abstract

Here, the 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/T³, but we formulate and test a slightmore »« less

Authors:

Wollaeger, Ryan T. ^[1]; Wollaber, Allan B. ^[1]; Urbatsch, Todd J. ^[1]; Densmore, Jeffery D. ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Bettis Atomic Power Lab., West Mifflin, PA (United States)

Publication Date:: Tue Feb 23 00:00:00 EST 2016

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1255243

Report Number(s):: LA-UR-15-24303
Journal ID: ISSN 2332-4309

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational and Theoretical Transport

Additional Journal Information:: Journal Volume: 141; Journal Issue: C; Journal ID: ISSN 2332-4309

Publisher:: Taylor and Francis

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; radiation, transport, methods

Citation Formats


                    Wollaeger, Ryan T., Wollaber, Allan B., Urbatsch, Todd J., and Densmore, Jeffery D. Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity.  United States: N. p., 2016. 
Web.  doi:10.1080/23324309.2016.1157491.

Copy to clipboard


                    Wollaeger, Ryan T., Wollaber, Allan B., Urbatsch, Todd J., & Densmore, Jeffery D. Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity.  United States.  https://doi.org/10.1080/23324309.2016.1157491

Copy to clipboard


                    Wollaeger, Ryan T., Wollaber, Allan B., Urbatsch, Todd J., and Densmore, Jeffery D. Tue .  
"Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity".  United States.  https://doi.org/10.1080/23324309.2016.1157491.  https://www.osti.gov/servlets/purl/1255243.

Copy to clipboard


                    
@article{osti_1255243,

  title        = {Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity},

  author       = {Wollaeger, Ryan T. and Wollaber, Allan B. and Urbatsch, Todd J. and Densmore, Jeffery D.},

  abstractNote = {Here, the 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/T3, but we formulate and test a slight extension for opacities ~ 1/T3.5, 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.},

  doi          = {10.1080/23324309.2016.1157491},

  journal      = {Journal of Computational and Theoretical Transport},

  number       = C,

  volume       = 141,

  place        = {United States},

  year         = {Tue Feb 23 00:00:00 EST 2016},

  month        = {Tue Feb 23 00:00:00 EST 2016}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1080/23324309.2016.1157491

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 6 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

An implicit Monte Carlo scheme for calculating time and frequency dependent nonlinear radiation transport
journal, December 1971

Fleck, J. A.; Cummings, J. D.
Journal of Computational Physics, Vol. 8, Issue 3
DOI: 10.1016/0021-9991(71)90015-5

A random walk procedure for improving the computational efficiency of the implicit Monte Carlo method for nonlinear radiation transport
journal, June 1984

Fleck, J. A.; Canfield, E. H.
Journal of Computational Physics, Vol. 54, Issue 3
DOI: 10.1016/0021-9991(84)90130-x

Asymptotic analysis of the spatial discretization of radiation absorption and re-emission in Implicit Monte Carlo
journal, February 2011

Densmore, Jeffery D.
Journal of Computational Physics, Vol. 230, Issue 4
DOI: 10.1016/j.jcp.2010.10.030

Similar Records in DOE PAGES and OSTI.GOV collections:

An Analysis of Source Tilting and Sub-cell Opacity Sampling for IMC

Technical Report Wollaeger, Ryan T. ; Urbatsch, Todd J. ; Wollaber, Allan B. ; ...

Implicit Monte Carlo (IMC) is a stochastic method for solving the radiative transfer equations for multiphysics application with the material in local thermodynamic equilibrium. The IMC method employs a fictitious scattering term that is computed from an implicit discretization of the material temperature equation. Unfortunately, the original histogram representation of the temperature and opacity with respect to the spatial domain leads to nonphysically fast propagation of radiation waves through optically thick material. In the past, heuristic source tilting schemes have been used to mitigate the numerical teleportation error of the radiation particles in IMC that cause this overly rapid radiationmore »« less
https://doi.org/10.2172/1047094

Full Text Available
MILAGRO IMPLICIT MONTE CARLO: NEW CAPABILITIES AND RESULTS

Conference URBATSCH, T ; EVANS, T

Milagro is a stand-alone, radiation-only, code that performs nonlinear radiative transfer calculations using the Fleck and Cummings method of Implicit Monte Carlo (IMC). Milagro is an object-oriented, C++ code that utilizes classes in our group's (CCS-4) radiation transport library. Milagro and its underlying classes have been significantly upgraded since 1998, when results from Milagro were first presented. Most notably, the object-oriented design has been revised to allow for optimal stand-alone parallel efficiency and rapid integration of new classes. For example, the better design, coupled with stringent component testing, allowed for immediate integration of the full domain decomposition parallel scheme. (Itmore »« less
Full Text Available
Including the effects of temperature-dependent opacities in the implicit Monte Carlo algorithm

Journal Article Gentile, N.A., E-mail: gentile1@llnl.go - Journal of Computational Physics

The Implicit Monte Carlo technique of Fleck and Cummings is often employed to numerically simulate radiative transfer. This method achieves greater stability than one with a fully explicit time discretization by estimating the t{sup n+1} value of T{sup 4} from the thermal emission term, which is proportional to T{sup 4}. In the Fleck and Cummings algorithm, this results in decreasing the absorption by the so-called 'Fleck factor', and adding a corresponding amount of effective scattering. We show how to include the effects of the temperature-dependent opacity to the estimated t{sup n+1} value of the thermal emission term. This results inmore »« less
https://doi.org/10.1016/j.jcp.2011.03.029
Reduced Variance for Material Sources in Implicit Monte Carlo

Conference Urbatsch, Todd J

Implicit Monte Carlo (IMC), a time-implicit method due to Fleck and Cummings, is used for simulating supernovae and inertial confinement fusion (ICF) systems where x-rays tightly and nonlinearly interact with hot material. The IMC algorithm represents absorption and emission within a timestep as an effective scatter. Similarly, the IMC time-implicitness splits off a portion of a material source directly into the radiation field. We have found that some of our variance reduction and particle management schemes will allow large variances in the presence of small, but important, material sources, as in the case of ICF hot electron preheat sources. Wemore »« less
Full Text Available
A modified implicit Monte Carlo method for time-dependent radiative transfer with adaptive material coupling

Journal Article McClarren, Ryan G. ; Urbatsch, Todd J. - Journal of Computational Physics

In this paper we develop a robust implicit Monte Carlo (IMC) algorithm based on more accurately updating the linearized equilibrium radiation energy density. The method does not introduce oscillations in the solution and has the same limit as {delta}t{yields}{infinity} as the standard Fleck and Cummings IMC method. Moreover, the approach we introduce can be trivially added to current implementations of IMC by changing the definition of the Fleck factor. Using this new method we develop an adaptive scheme that uses either standard IMC or the modified method basing the adaptation on a zero-dimensional problem solved in each cell. Numerical resultsmore »« less
https://doi.org/10.1016/j.jcp.2009.04.028

Similar Records

Title: Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity

Abstract

Citation Formats

An implicit Monte Carlo scheme for calculating time and frequency dependent nonlinear radiation transport journal, December 1971

A random walk procedure for improving the computational efficiency of the implicit Monte Carlo method for nonlinear radiation transport journal, June 1984

Asymptotic analysis of the spatial discretization of radiation absorption and re-emission in Implicit Monte Carlo journal, February 2011

An implicit Monte Carlo scheme for calculating time and frequency dependent nonlinear radiation transport
journal, December 1971

A random walk procedure for improving the computational efficiency of the implicit Monte Carlo method for nonlinear radiation transport
journal, June 1984

Asymptotic analysis of the spatial discretization of radiation absorption and re-emission in Implicit Monte Carlo
journal, February 2011