Four decades of implicit Monte Carlo
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.
- Publication Date:
- Report Number(s):
- LA-UR-15-23553
Journal ID: ISSN 2332-4309
- Grant/Contract Number:
- AC52-06NA25396
- Type:
- 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
- Research Org:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org:
- USDOE
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; 97 MATHEMATICS AND COMPUTING; Monte Carlo, radiative transfer, HEDP
- OSTI Identifier:
- 1255843
Wollaber, Allan B. Four decades of implicit Monte Carlo. United States: N. p.,
Web. doi:10.1080/23324309.2016.1138132.
Wollaber, Allan B. Four decades of implicit Monte Carlo. United States. doi:10.1080/23324309.2016.1138132.
Wollaber, Allan B. 2016.
"Four decades of implicit Monte Carlo". United States.
doi: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},
journal = {Journal of Computational and Theoretical Transport},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {2}
}