Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise nonconstant opacity
Here, the nonlinear thermal radiativetransfer 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 piecewiseconstant material properties. For domains with a coarse spatial grid and large temperature gradients, an error known as numerical teleportation may cause artificially noncausal energy propagation and consequently an inaccurate material temperature. Source tilting is a technique to reduce teleportation error by constructing subspatialcell (or subcell) 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 temperaturedependent 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 tiltdependent opacity can introduce another dominant error that overly inhibits thermal wavefronts. We show that we can mitigate both teleportation and underpropagation 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 amore »
 Authors:

^{[1]};
^{[1]};
^{[1]};
^{[2]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Bettis Atomic Power Lab., West Mifflin, PA (United States)
 Publication Date:
 Report Number(s):
 LAUR1524303
Journal ID: ISSN 23324309
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational and Theoretical Transport
 Additional Journal Information:
 Journal Volume: 141; Journal Issue: C; Journal ID: ISSN 23324309
 Publisher:
 Taylor and Francis
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; radiation, transport, methods
 OSTI Identifier:
 1255243
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 nonconstant opacity. United States: N. p.,
Web. doi:10.1080/23324309.2016.1157491.
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 nonconstant opacity. United States. doi:10.1080/23324309.2016.1157491.
Wollaeger, Ryan T., Wollaber, Allan B., Urbatsch, Todd J., and Densmore, Jeffery D.. 2016.
"Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise nonconstant opacity". United States.
doi:10.1080/23324309.2016.1157491. https://www.osti.gov/servlets/purl/1255243.
@article{osti_1255243,
title = {Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise nonconstant opacity},
author = {Wollaeger, Ryan T. and Wollaber, Allan B. and Urbatsch, Todd J. and Densmore, Jeffery D.},
abstractNote = {Here, the nonlinear thermal radiativetransfer 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 piecewiseconstant material properties. For domains with a coarse spatial grid and large temperature gradients, an error known as numerical teleportation may cause artificially noncausal energy propagation and consequently an inaccurate material temperature. Source tilting is a technique to reduce teleportation error by constructing subspatialcell (or subcell) 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 temperaturedependent 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 tiltdependent opacity can introduce another dominant error that overly inhibits thermal wavefronts. We show that we can mitigate both teleportation and underpropagation 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 piecewiseconstant material temperature updates.},
doi = {10.1080/23324309.2016.1157491},
journal = {Journal of Computational and Theoretical Transport},
number = C,
volume = 141,
place = {United States},
year = {2016},
month = {2}
}