Four decades of implicit Monte Carlo

Wollaber, Allan B.

doi:10.1080/23324309.2016.1138132

Four decades of implicit Monte Carlo

Journal Article · Tue Feb 23 00:00:00 EST 2016 · Journal of Computational and Theoretical Transport

DOI:https://doi.org/10.1080/23324309.2016.1138132· OSTI ID:1255843

Wollaber, Allan B. ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1255843

Report Number(s):: LA-UR-15-23553

Journal Information:: Journal of Computational and Theoretical Transport, Journal Name: Journal of Computational and Theoretical Transport; ISSN 2332-4309

Publisher:: Taylor and FrancisCopyright Statement

Country of Publication:: United States

Language:: English

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79 ASTRONOMY AND ASTROPHYSICS
97 MATHEMATICS AND COMPUTING
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Four decades of implicit Monte Carlo

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