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Title: Adjoint-based sensitivity analysis for high-energy density radiative transfer using flux-limited diffusion

Authors:
ORCiD logo; ORCiD logo
Publication Date:
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1397472
Grant/Contract Number:
NA0002376
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
High Energy Density Physics
Additional Journal Information:
Journal Volume: 22; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-10-04 21:04:48; Journal ID: ISSN 1574-1818
Publisher:
Elsevier
Country of Publication:
Netherlands
Language:
English

Citation Formats

Humbird, Kelli D., and McClarren, Ryan G.. Adjoint-based sensitivity analysis for high-energy density radiative transfer using flux-limited diffusion. Netherlands: N. p., 2017. Web. doi:10.1016/j.hedp.2016.12.002.
Humbird, Kelli D., & McClarren, Ryan G.. Adjoint-based sensitivity analysis for high-energy density radiative transfer using flux-limited diffusion. Netherlands. doi:10.1016/j.hedp.2016.12.002.
Humbird, Kelli D., and McClarren, Ryan G.. Wed . "Adjoint-based sensitivity analysis for high-energy density radiative transfer using flux-limited diffusion". Netherlands. doi:10.1016/j.hedp.2016.12.002.
@article{osti_1397472,
title = {Adjoint-based sensitivity analysis for high-energy density radiative transfer using flux-limited diffusion},
author = {Humbird, Kelli D. and McClarren, Ryan G.},
abstractNote = {},
doi = {10.1016/j.hedp.2016.12.002},
journal = {High Energy Density Physics},
number = C,
volume = 22,
place = {Netherlands},
year = {Wed Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.hedp.2016.12.002

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  • 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 time-dependent non-equilibrium 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 non-equilibrium radiation wave front. In addition, the DP{sub 0} approximation should be more accurate in non-equilibrium optically thin regions where the positive and negative angular domains are largely decoupled. We developmore » an adaptive angular technique that locally uses either the DP{sub 0} or P{sub 1} flux-limited diffusion approximation depending on the degree to which the radiation and material fields are in thermodynamic equilibrium. Numerical results are presented for two test problems due to Su and Olson and to Ganapol and Pomraning for which semi-analytic transport solutions exist. These numerical results demonstrate that the adaptive P{sub 1}-DP{sub 0} diffusion approximation can yield improvements in accuracy over the standard P{sub 1} diffusion approximation, both without and with flux-limiting, for non-equilibrium grey radiative transfer.« less
  • 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 time-dependent non-equilibrium 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 non-equilibrium radiation wave front. In addition, the DP{sub 0} approximation should be more accurate in non-equilibrium optically thin regions where the positive and negative angular domains are largely decoupled. We developmore » an adaptive angular technique that locally uses either the DP{sub 0} or P{sub 1} flux-limited diffusion approximation depending on the degree to which the radiation and material fields are in thermodynamic equilibrium. Numerical results are presented for two test problems due to Su and Olson and to Ganapol and Pomraning for which semi-analytic transport solutions exist. These numerical results demonstrate that the adaptive P{sub 1}-DP{sub 0} diffusion approximation can yield improvements in accuracy over the standard P{sub 1} diffusion approximation, both without and with flux-limiting, for non-equilibrium grey radiative transfer.« less
  • The ability to perform sensitivity analyses using adjoint-based first-order sensitivity theory has existed for decades. This paper provides guidance on how adjoint sensitivity methods can be used to predict the effect of material density and composition uncertainties in critical experiments, including when these uncertain parameters are correlated or constrained. Two widely used Monte Carlo codes, MCNP6 (Ref. 2) and SCALE 6.2 (Ref. 3), are both capable of computing isotopic density sensitivities in continuous energy and angle. Additionally, Perkó et al. have shown how individual isotope density sensitivities, easily computed using adjoint methods, can be combined to compute constrained first-order sensitivitiesmore » that may be used in the uncertainty analysis. This paper provides details on how the codes are used to compute first-order sensitivities and how the sensitivities are used in an uncertainty analysis. Constrained first-order sensitivities are computed in a simple example problem.« less
  • The ability to perform sensitivity analyses using adjoint-based first-order sensitivity theory has existed for decades. This paper provides guidance on how adjoint sensitivity methods can be used to predict the effect of material density and composition uncertainties in critical experiments, including when these uncertain parameters are correlated or constrained. Two widely used Monte Carlo codes, MCNP6 (Ref. 2) and SCALE 6.2 (Ref. 3), are both capable of computing isotopic density sensitivities in continuous energy and angle. Additionally, Perkó et al. have shown how individual isotope density sensitivities, easily computed using adjoint methods, can be combined to compute constrained first-order sensitivitiesmore » that may be used in the uncertainty analysis. This paper provides details on how the codes are used to compute first-order sensitivities and how the sensitivities are used in an uncertainty analysis. Constrained first-order sensitivities are computed in a simple example problem.« less
  • The adjoint method of sensitivity analysis is demonstrated on a radiative-convective climate model. A single adjoint calculation, which requires about the same computation time as the original model, suffices to calculate sensitivities of surface air temperature to all 312 model parameters. The uses of these sensitivities are discussed and illustrated. The sensitivities accurately predict the effect on surface air temperature of small variations in the model parameters. Relative sensitivities are used to rank the importance of all the parameters. Several of the sensitivities to parameters customarily considered in previous works (e.g., solar constant, surface albedo, relative humidity, CO/sub 2/ concentration)more » are reproduced, but the largest sensitivities are to constants used to compute the saturation vapor pressure of water. The uncertainties in the model results are expressed formally in terms of all the sensitivities and parameter covariances. For results that cannot readily be compared with observation (for example, the results of a CO/sub 2/ doubling experiment), this method of uncertainty analysis is the only systematic way to estimate the reliability of model results. The radiative-convective model contains complex nonlinear processes of the type found in general circulation models. Therefore, the fact that the adjoint method works successfully and efficiently for the radiative-convective model provides valuable information about subsequent application of the method to general circulation models.« less