The equilibriumdiffusion limit for radiation hydrodynamics
Abstract
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:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Texas A & M Univ., College Station, TX (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1374348
 Report Number(s):
 LAUR1720878
Journal ID: ISSN 00224073
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Journal Article: 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
 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
Citation Formats
Ferguson, J. M., Morel, J. E., and Lowrie, R.. The equilibriumdiffusion limit for radiation hydrodynamics. United States: N. p., 2017.
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.
@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
}

A finite difference scheme is proposed for twodimensional radiation hydrodynamical equations in the transport limit. The scheme is of Godunovtype, in which the set of timeaveraged flux needed in the scheme is calculated through Riemann problems solved. In the scheme, flow signals are explicitly treated, while radiation signals are implicitly treated. Flow fields and radiation fields are updated simultaneously. An iterative approach is proposed to solve the set of nonlinear algebraic equations arising from the implicitness of the scheme. The sweeping method used in the scheme significantly reduces the number of iterations or computer CPU time needed. A new approachmore »

THE GENERAL RELATIVISTIC EQUATIONS OF RADIATION HYDRODYNAMICS IN THE VISCOUS LIMIT
We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energymomentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the fourvelocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and domore » 
Entropybased artificial viscosity stabilization for nonequilibrium Grey RadiationHydrodynamics
The entropy viscosity method is extended to the nonequilibrium Grey RadiationHydrodynamic equations. The method employs a viscous regularization to stabilize the numerical solution. The artificial viscosity coefficient is modulated by the entropy production and peaks at shock locations. The added dissipative terms are consistent with the entropy minimum principle. A new functional form of the entropy residual, suitable for the RadiationHydrodynamic equations, is derived. We demonstrate that the viscous regularization preserves the equilibrium diffusion limit. The equations are discretized with a standard Continuous Galerkin Finite Element Method and a fully implicit temporal integrator within the MOOSE multiphysics framework. The methodmore » 
Fluxlimited diffusion models in radiation hydrodynamics
The authors discuss certain fluxlimited diffusion theories which approximately describe radiative transfer in the presence of steep spatial gradients. A new formulation is presented which generalizes a fluxlimited description currently in widespread use for large radiation hydrodynamic calculations. This new formation allows more than one Case discrete mode to be described by a fluxlimited diffusion equation. Such behavior is not extant in existing formulations. Numerical results predicted by these fluxlimited diffusion models are presented for radiation penetration into an initially cold halfspace. 37 refs., 5 figs.