Stability analysis and time-step limits for a Monte Carlo Compton-scattering method

Authors:
Jeffery D. Densmore;James S. Warsa;Robert B. Lowrie
Affiliations:
Computational Physics and Methods Group, Los Alamos National Laboratory, P.O. Box 1663, MS D409, Los Alamos, NM 87545, USA;Computational Physics and Methods Group, Los Alamos National Laboratory, P.O. Box 1663, MS D409, Los Alamos, NM 87545, USA;Computational Physics and Methods Group, Los Alamos National Laboratory, P.O. Box 1663, MS D409, Los Alamos, NM 87545, USA
Venue:
Journal of Computational Physics
Year:
2010

Citing 4
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Solution of the nonlinear radiative transfer equations by a fully implicit matrix Monte Carlo method coupled with the Rosseland diffusion equation via domain decomposition

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Abstract

A Monte Carlo method for simulating Compton scattering in high energy density applications has been presented that models the photon-electron collision kinematics exactly [E. Canfield, W.M. Howard, E.P. Liang, Inverse Comptonization by one-dimensional relativistic electrons, Astrophys. J. 323 (1987) 565]. However, implementing this technique typically requires an explicit evaluation of the material temperature, which can lead to unstable and oscillatory solutions. In this paper, we perform a stability analysis of this Monte Carlo method and develop two time-step limits that avoid undesirable behavior. The first time-step limit prevents instabilities, while the second, more restrictive time-step limit avoids both instabilities and nonphysical oscillations. With a set of numerical examples, we demonstrate the efficacy of these time-step limits.