Derivation and Solution of Multifrequency Radiation Diffusion Equations for Homogeneous Refractive Lossy Media [electronic resource].

Published: Washington, D.C. : United States. Dept. of Energy, 2010.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
Physical Description: PDF-file: 29 pages; size: 0.4 Mbytes
Additional Creators: Lawrence Berkeley National Laboratory, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information

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Summary

Starting from the radiation transport equation for homogeneous, refractive lossy media, we derive the corresponding time-dependent multifrequency diffusion equations. Zeroth and first moments of the transport equation couple the energy density, flux and pressure tensor. The system is closed by neglecting the temporal derivative of the flux and replacing the pressure tensor by its diagonal analogue. The system is coupled to a diffusion equation for the matter temperature. We are interested in modeling annealing of silica (SiO₂). We derive boundary conditions at a planar air-silica interface taking account of reflectivities. The spectral dimension is discretized into a finite number of intervals leading to a system of multigroup diffusion equations. Three simulations are presented. One models cooling of a silica slab, initially at 2500 K, for 10 s. The other two are 1D and 2D simulations of irradiating silica with a CO₂ laser, λ = 10.59 {micro}m. In 2D, we anneal a disk (radius = 0.4, thickness = 0.4 cm) with a laser, Gaussian profile (r₀ = 0.5 mm for 1/e decay).

Report Numbers

E 1.99:llnl-jrnl-422310
llnl-jrnl-422310

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Published through SciTech Connect.
01/05/2010.
"llnl-jrnl-422310"
Journal of Computational Physics, vol. 230, no. 4, February 20, 2011, pp. 984-999 230 4 ISSN 0021-9991; JCTPAH FT
Stolken, J S; Shestakov, A I; Vignes, R M.

Funding Information

W-7405-ENG-48

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