Asymptotic equilibrium diffusion analysis of time-dependent Monte Carlo methods for grey radiative transfer
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...... Asymptotic equilibrium diffusion limit Even in the absence of spatial grid effects, the IMC equations do not preserve the “asymptotic equilibrium diffusion limit” due to the linearization error (Densmore and Larsen, 2004)....
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...…are unconditionally stable and monotone, that the time-dependent source and effective scattering terms can be implemented efficiently, and that there are cases for which they preserve the equilibrium diffusion limit (Cheatham, 2010; Densmore and Larsen, 2004; Martin and Brown, 2002, 2001c;…...
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...This approach does contain temporal truncation errors due to usingT 4 n+1 as the emission term and time-explicit data for the opacities and emission spectrum, but, because it rigorously treats the nonlinearity, it preserves the thick diffusion limit (Densmore and Larsen, 2004)....
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...It can be shown that theCarter-Forest equations are temporally exact for linear problems, that they are unconditionally stable and monotone, that the time-dependent source and effective scattering terms can be implemented efficiently, and that there are cases for which they preserve the equilibrium diffusion limit (Cheatham, 2010; Densmore and Larsen, 2004; Martin and Brown, 2002, 2001c; Wollaber and Larsen, 2011)....
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...This approach does contain temporal truncation errors due to usingT 4n+1 as the emission term and time-explicit data for the opacities and emission spectrum, but, because it rigorously treats the nonlinearity, it preserves the thick diffusion limit (Densmore and Larsen, 2004)....
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