Nonrelativistic grey S n transport radiativeshock solutions
Abstract
We present semianalytic radiativeshock solutions in which grey Sntransport is used to model the radiation, and we include both constant cross sections and cross sections that depend on temperature and density. These new solutions solve for a variable Eddington factor (VEF) across the shock domain, which allows for interesting physics not seen before in radiativeshock solutions. Comparisons are made with the grey nonequilibriumdiffusion radiativeshock solutions of Lowrie and Edwards [1], which assumed that the Eddington factor is constant across the shock domain. It is our experience that the local Mach number is monotonic when producing nonequilibriumdiffusion solutions, but that this monotonicity may disappear while integrating the precursor region to produce Sntransport solutions. For temperature and densitydependent cross sections we show evidence of a spike in the VEF in the far upstream portion of the radiativeshock precursor. We show evidence of an adaptation zone in the precursor region, adjacent to the embedded hydrodynamic shock, as conjectured by Drake [2, 3], and also confirm his expectation that the precursor temperatures adjacent to the Zel’dovich spike take values that are greater than the downstream postshock equilibrium temperature. We also show evidence that the radiation energy density can be nonmonotonic under the Zel’dovich spike,more »
 Authors:
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1345943
 Alternate Identifier(s):
 OSTI ID: 1397411
 Report Number(s):
 LAUR1628784
Journal ID: ISSN 15741818; TRN: US1700519
 Grant/Contract Number:
 AC5206NA25396; AC5206NA25396 as LAUR1628784
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 High Energy Density Physics
 Additional Journal Information:
 Journal Volume: 23; Journal Issue: C; Journal ID: ISSN 15741818
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; radiation hydrodynamics; variable Eddington factor; radiativeshock solutions; antidiffusion
Citation Formats
Ferguson, J. M., Morel, J. E., and Lowrie, R. B.. Nonrelativistic grey S n transport radiativeshock solutions. United States: N. p., 2017.
Web. doi:10.1016/j.hedp.2017.02.010.
Ferguson, J. M., Morel, J. E., & Lowrie, R. B.. Nonrelativistic grey S n transport radiativeshock solutions. United States. doi:10.1016/j.hedp.2017.02.010.
Ferguson, J. M., Morel, J. E., and Lowrie, R. B.. 2017.
"Nonrelativistic grey S n transport radiativeshock solutions". United States.
doi:10.1016/j.hedp.2017.02.010.
@article{osti_1345943,
title = {Nonrelativistic grey S n transport radiativeshock solutions},
author = {Ferguson, J. M. and Morel, J. E. and Lowrie, R. B.},
abstractNote = {We present semianalytic radiativeshock solutions in which grey Sntransport is used to model the radiation, and we include both constant cross sections and cross sections that depend on temperature and density. These new solutions solve for a variable Eddington factor (VEF) across the shock domain, which allows for interesting physics not seen before in radiativeshock solutions. Comparisons are made with the grey nonequilibriumdiffusion radiativeshock solutions of Lowrie and Edwards [1], which assumed that the Eddington factor is constant across the shock domain. It is our experience that the local Mach number is monotonic when producing nonequilibriumdiffusion solutions, but that this monotonicity may disappear while integrating the precursor region to produce Sntransport solutions. For temperature and densitydependent cross sections we show evidence of a spike in the VEF in the far upstream portion of the radiativeshock precursor. We show evidence of an adaptation zone in the precursor region, adjacent to the embedded hydrodynamic shock, as conjectured by Drake [2, 3], and also confirm his expectation that the precursor temperatures adjacent to the Zel’dovich spike take values that are greater than the downstream postshock equilibrium temperature. We also show evidence that the radiation energy density can be nonmonotonic under the Zel’dovich spike, which is indicative of antidiffusive radiation flow as predicted by McClarren and Drake [4]. We compare the angle dependence of the radiation flow for the Sntransport and nonequilibriumdiffusion radiation solutions, and show that there are considerable differences in the radiation flow between these models across the shock structure. Lastly, we analyze the radiation flow to understand the cause of the adaptation zone, as well as the structure of the Sntransport radiationintensity solutions across the shock structure.},
doi = {10.1016/j.hedp.2017.02.010},
journal = {High Energy Density Physics},
number = C,
volume = 23,
place = {United States},
year = 2017,
month = 6
}

Angularly Adaptive P1Double P0 FluxLimited Diffusion Solutions of NonEquilibrium Grey Radiative Transfer Problems
The double spherical harmonics angular approximation in the lowest order, i.e. double P{sub 0} (DP{sub 0}), is developed for the solution of timedependent nonequilibrium grey radiative transfer problems in planar geometry. Although the DP{sub 0} diffusion approximation is expected to be less accurate than the P{sub 1} diffusion approximation at and near thermodynamic equilibrium, the DP{sub 0} angular approximation can more accurately capture the complicated angular dependence near a nonequilibrium radiation wave front. In addition, the DP{sub 0} approximation should be more accurate in nonequilibrium optically thin regions where the positive and negative angular domains are largely decoupled. We developmore » 
Angularly Adaptive P1  Double P0 FluxLimited Diffusion Solutions of NonEquilibrium Grey Radiative Transfer Problems
The double spherical harmonics angular approximation in the lowest order, i.e. double P{sub 0} (DP{sub 0}), is developed for the solution of timedependent nonequilibrium grey radiative transfer problems in planar geometry. Although the DP{sub 0} diffusion approximation is expected to be less accurate than the P{sub 1} diffusion approximation at and near thermodynamic equilibrium, the DP{sub 0} angular approximation can more accurately capture the complicated angular dependence near a nonequilibrium radiation wave front. In addition, the DP{sub 0} approximation should be more accurate in nonequilibrium optically thin regions where the positive and negative angular domains are largely decoupled. We developmore »