The equilibrium-diffusion limit for radiation hydrodynamics

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

doi:10.1016/j.jqsrt.2017.07.031

Title: The equilibrium-diffusion limit for radiation hydrodynamics

Journal Article · Thu Jul 27 00:00:00 EDT 2017 · Journal of Quantitative Spectroscopy and Radiative Transfer

DOI:https://doi.org/10.1016/j.jqsrt.2017.07.031· OSTI ID:1374348

Ferguson, J. M. ^[1]; Morel, J. E. ^[2];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Texas A & M Univ., College Station, TX (United States)

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (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 equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy. Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source 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 first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396; LA-UR-17-20878

OSTI ID:: 1374348

Alternate ID(s):: OSTI ID: 1549617

Report Number(s):: LA-UR-17-20878

Journal Information:: Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 202, Issue C; ISSN 0022-4073

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 10 works

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References (22)

The Coupling of Radiation and Hydrodynamics Lowrie, R. B.; Morel, J. E.; Hittinger, J. A. The Astrophysical Journal, Vol. 521, Issue 1 https://doi.org/10.1086/307515	journal	August 1999
Uniform asymptotic expansions in transport theory with small mean free paths, and the diffusion approximation Habetler, G. J.; Matkowsky, B. J. Journal of Mathematical Physics, Vol. 16, Issue 4 https://doi.org/10.1063/1.522618	journal	April 1975
Neutron transport and diffusion in inhomogeneous media. I Larsen, Edward W. Journal of Mathematical Physics, Vol. 16, Issue 7 https://doi.org/10.1063/1.522714	journal	July 1975
Asymptotic analysis of radiative transfer problems Larsen, E. W.; Pomraning, G. C.; Badham, V. C. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 29, Issue 4 https://doi.org/10.1016/0022-4073(83)90048-1	journal	April 1983
Diffusion-limit asymptotics of the transport equation, the P1/3 equations, and two flux-limited diffusion theories Morel, J. E. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 65, Issue 5 https://doi.org/10.1016/S0022-4073(99)00148-X	journal	June 2000
Initial and boundary conditions for diffusive linear transport problems Malvagi, F.; Pomraning, G. C. Journal of Mathematical Physics, Vol. 32, Issue 3 https://doi.org/10.1063/1.529374	journal	March 1991
Asymptotic solution of neutron transport problems for small mean free paths Larsen, Edward W.; Keller, Joseph B. Journal of Mathematical Physics, Vol. 15, Issue 1 https://doi.org/10.1063/1.1666510	journal	January 1974
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes Larsen, Edward W.; Morel, J. E.; Miller, Warren F. Journal of Computational Physics, Vol. 69, Issue 2 https://doi.org/10.1016/0021-9991(87)90170-7	journal	April 1987
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II larsen, Edward W.; Morel, J. E. Journal of Computational Physics, Vol. 83, Issue 1 https://doi.org/10.1016/0021-9991(89)90229-5	journal	July 1989
Characteristic Methods in Thick Diffusive Problems Adams, Marvin L.; Wareing, Todd A.; Walters, Wallace F. Nuclear Science and Engineering, Vol. 130, Issue 1 https://doi.org/10.13182/NSE98-A1987	journal	September 1998
Discontinuous Finite Element Transport Solutions in Thick Diffusive Problems Adams, Marvin L. Nuclear Science and Engineering, Vol. 137, Issue 3 https://doi.org/10.13182/NSE00-41	journal	March 2001
Asymptotic Analysis of Nonlinear Marshak Waves Larsen, E. W.; Pomraning, G. C. SIAM Journal on Applied Mathematics, Vol. 39, Issue 2 https://doi.org/10.1137/0139018	journal	October 1980
A Linear-Discontinuous Spatial Differencing Scheme forSnRadiative Transfer Calculations Morel, J. E.; Wareing, Todd A.; Smith, Kenneth Journal of Computational Physics, Vol. 128, Issue 2 https://doi.org/10.1006/jcph.1996.0223	journal	October 1996
Asymptotic Analysis of a Computational Method for Time- and Frequency-Dependent Radiative Transfer Adams, Marvin L.; Nowak, Paul F. Journal of Computational Physics, Vol. 146, Issue 1 https://doi.org/10.1006/jcph.1998.6063	journal	October 1998
Diffusion, P1, and other approximate forms of radiation transport Olson, Gordon L.; Auer, Lawrence H.; Hall, Michael L. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 64, Issue 6 https://doi.org/10.1016/S0022-4073(99)00150-8	journal	March 2000
Asymptotic equilibrium diffusion analysis of time-dependent Monte Carlo methods for grey radiative transfer Densmore, Jeffery D.; Larsen, Edward W. Journal of Computational Physics, Vol. 199, Issue 1 https://doi.org/10.1016/j.jcp.2004.02.004	journal	September 2004
Asymptotic analysis of the spatial discretization of radiation absorption and re-emission in Implicit Monte Carlo Densmore, Jeffery D. Journal of Computational Physics, Vol. 230, Issue 4 https://doi.org/10.1016/j.jcp.2010.10.030	journal	February 2011
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations Jin, Shi SIAM Journal on Scientific Computing, Vol. 21, Issue 2 https://doi.org/10.1137/S1064827598334599	journal	January 1999
Radiative shock solutions with grey nonequilibrium diffusion Lowrie, Robert B.; Edwards, Jarrod D. Shock Waves, Vol. 18, Issue 2 https://doi.org/10.1007/s00193-008-0143-0	journal	May 2008
Radiative shock solutions in the equilibrium diffusion limit Lowrie, Robert B.; Rauenzahn, Rick M. Shock Waves, Vol. 16, Issue 6 https://doi.org/10.1007/s00193-007-0081-2	journal	May 2007
Issues with high-resolution Godunov methods for radiation hydrodynamics Lowrie, R. B.; Morel, J. E. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 69, Issue 4 https://doi.org/10.1016/S0022-4073(00)00097-2	journal	May 2001
On the Solution of the Time-Dependent inertial-Frame Equation of radiative Transfer in Moving Media to Mihalas, Dimitri; Klein, Richard I. Journal of Computational Physics, Vol. 46, Issue 1 https://doi.org/10.1016/0021-9991(82)90007-9	journal	August 1982

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Title: The equilibrium-diffusion limit for radiation hydrodynamics

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