Derivation and Solution of Multifrequency Radiation Diffusion Equations for Homogeneous Refractive Lossy Media
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 (SiO{sub 2}). 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 CO{sub 2} laser, {lambda} = 10.59 {micro}m. In 2D, we anneal a disk (radius = 0.4, thickness = 0.4 cm) with a laser, Gaussian profile (r{sub 0} = 0.5 mm for 1/e decay).
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 1020325
- Report Number(s):
- LLNL-JRNL-422310; JCTPAH; TRN: US201116%%260
- Journal Information:
- Journal of Computational Physics, Vol. 230, Issue 4; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
Multifrequency radiation diffusion equations for homogeneous, refractive, lossy media and their interface conditions
Stellar core collapse: Numerical model and infall epoch