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

Journal Article · Sun Feb 20 00:00:00 EST 2011 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.10.030· OSTI ID:21499766

Densmore, Jeffery D., E-mail: [e-mail] ^[1]

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1. Computational Physics and Methods Group, Los Alamos National Laboratory, P.O. Box 1663, MS D409, Los Alamos, NM 87545 (United States)

We perform an asymptotic analysis of the spatial discretization of radiation absorption and re-emission in Implicit Monte Carlo (IMC), a Monte Carlo technique for simulating nonlinear radiative transfer. Specifically, we examine the approximation of absorption and re-emission by a spatially continuous artificial-scattering process and either a piecewise-constant or piecewise-linear emission source within each spatial cell. We consider three asymptotic scalings representing (i) a time step that resolves the mean-free time, (ii) a Courant limit on the time-step size, and (iii) a fixed time step that does not depend on any asymptotic scaling. For the piecewise-constant approximation, we show that only the third scaling results in a valid discretization of the proper diffusion equation, which implies that IMC may generate inaccurate solutions with optically large spatial cells if time steps are refined. However, we also demonstrate that, for a certain class of problems, the piecewise-linear approximation yields an appropriate discretized diffusion equation under all three scalings. We therefore expect IMC to produce accurate solutions for a wider range of time-step sizes when the piecewise-linear instead of piecewise-constant discretization is employed. We demonstrate the validity of our analysis with a set of numerical examples.

• OSTI ID: 21499766
• Journal Information: Journal of Computational Physics, Vol. 230, Issue 4; Other Information: DOI: 10.1016/j.jcp.2010.10.030; PII: S0021-9991(10)00586-3; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ABSORPTION
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
DIFFUSION EQUATIONS
MATHEMATICAL MODELS
MONTE CARLO METHOD
NONLINEAR PROBLEMS
RADIANT HEAT TRANSFER
SCATTERING
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ENERGY TRANSFER
EQUATIONS
HEAT TRANSFER
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
SORPTION