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Title: Four decades of implicit Monte Carlo

Abstract

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. Here, we consider spatial accuracy limitations of the IMC equations and discussion acceleration and variance reduction techniques.

Authors:
 [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1255843
Report Number(s):
LA-UR-15-23553
Journal ID: ISSN 2332-4309
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational and Theoretical Transport
Additional Journal Information:
Journal Name: Journal of Computational and Theoretical Transport; Journal ID: ISSN 2332-4309
Publisher:
Taylor and Francis
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; 97 MATHEMATICS AND COMPUTING; Monte Carlo, radiative transfer, HEDP

Citation Formats

Wollaber, Allan B. Four decades of implicit Monte Carlo. United States: N. p., 2016. Web. doi:10.1080/23324309.2016.1138132.
Wollaber, Allan B. Four decades of implicit Monte Carlo. United States. https://doi.org/10.1080/23324309.2016.1138132
Wollaber, Allan B. 2016. "Four decades of implicit Monte Carlo". United States. https://doi.org/10.1080/23324309.2016.1138132. https://www.osti.gov/servlets/purl/1255843.
@article{osti_1255843,
title = {Four decades of implicit Monte Carlo},
author = {Wollaber, Allan B.},
abstractNote = {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. Here, we consider spatial accuracy limitations of the IMC equations and discussion acceleration and variance reduction techniques.},
doi = {10.1080/23324309.2016.1138132},
url = {https://www.osti.gov/biblio/1255843}, journal = {Journal of Computational and Theoretical Transport},
issn = {2332-4309},
number = ,
volume = ,
place = {United States},
year = {Tue Feb 23 00:00:00 EST 2016},
month = {Tue Feb 23 00:00:00 EST 2016}
}

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Cited by: 32 works
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Works referencing / citing this record:

Monte Carlo radiative transfer
journal, June 2019