The equilibriumdiffusion limit for radiation hydrodynamics
The equilibriumdiffusion approximation (EDA) is used to describe certain radiationhydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibriumdiffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both firstorder accurate with transport corrections occurring at second order. Having established the EDA’s firstorder accuracy we then analyze the grey nonequilibriumdiffusion approximation and the grey Eddington approximation and show that they both preserve this firstorder accuracy. Further, these approximations preserve the EDA’s firstorder accuracy when made in either the comovingframe (CMF) or the labframe (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiationsource equations are equivalent when neglecting O(β ^{2}) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this firstorder accuracy will not retain the correct equilibriumdiffusion solutions. As a practical example, we show that nonequilibriumdiffusion radiativeshock solutions devolve to equilibriumdiffusion solutions when the asymptotic parametermore »
 Authors:

^{[1]};
^{[2]};
^{[1]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Texas A & M Univ., College Station, TX (United States)
 Publication Date:
 Report Number(s):
 LAUR1720878
Journal ID: ISSN 00224073
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Quantitative Spectroscopy and Radiative Transfer
 Additional Journal Information:
 Journal Volume: 202; Journal Issue: C; Journal ID: ISSN 00224073
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Asymptotics; Equilibrium diffusion; Radiation transport; Radiation hydrodynamics; Grey nonequilibriumdiffusion approximation; Grey Eddington approximation; Radiativeshock solutions
 OSTI Identifier:
 1374348
Ferguson, J. M., Morel, J. E., and Lowrie, R.. The equilibriumdiffusion limit for radiation hydrodynamics. United States: N. p.,
Web. doi:10.1016/j.jqsrt.2017.07.031.
Ferguson, J. M., Morel, J. E., & Lowrie, R.. The equilibriumdiffusion limit for radiation hydrodynamics. United States. doi:10.1016/j.jqsrt.2017.07.031.
Ferguson, J. M., Morel, J. E., and Lowrie, R.. 2017.
"The equilibriumdiffusion limit for radiation hydrodynamics". United States.
doi:10.1016/j.jqsrt.2017.07.031. https://www.osti.gov/servlets/purl/1374348.
@article{osti_1374348,
title = {The equilibriumdiffusion limit for radiation hydrodynamics},
author = {Ferguson, J. M. and Morel, J. E. and Lowrie, R.},
abstractNote = {The equilibriumdiffusion approximation (EDA) is used to describe certain radiationhydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibriumdiffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both firstorder accurate with transport corrections occurring at second order. Having established the EDA’s firstorder accuracy we then analyze the grey nonequilibriumdiffusion approximation and the grey Eddington approximation and show that they both preserve this firstorder accuracy. Further, these approximations preserve the EDA’s firstorder accuracy when made in either the comovingframe (CMF) or the labframe (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiationsource equations are equivalent when neglecting O(β2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this firstorder accuracy will not retain the correct equilibriumdiffusion solutions. As a practical example, we show that nonequilibriumdiffusion radiativeshock solutions devolve to equilibriumdiffusion solutions when the asymptotic parameter is small.},
doi = {10.1016/j.jqsrt.2017.07.031},
journal = {Journal of Quantitative Spectroscopy and Radiative Transfer},
number = C,
volume = 202,
place = {United States},
year = {2017},
month = {7}
}