scholarly journals Nonlinear Elimination Applied to Radiation Diffusion

2020 ◽  
Vol 194 (11) ◽  
pp. 939-951
Author(s):  
Thomas A. Brunner ◽  
Terry S. Haut ◽  
Paul F. Nowak
Keyword(s):  
Radiation Diffusion ◽  
Nonlinear Elimination

An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations

2015 ◽  
Vol 18 (5) ◽  
pp. 1313-1335 ◽  
Author(s):  
Xiaoqiang Yue ◽  
Shi Shu ◽  
Xiao wen Xu ◽  
Zhiyang Zhou
Keyword(s):  
Convergence Analysis ◽  
Estimation Theory ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Condition Numbers ◽  
Radiation Diffusion ◽  
Discrete Problems ◽  
Preconditioned Gmres

AbstractThe paper aims to develop an effective preconditioner and conduct the convergence analysis of the corresponding preconditioned GMRES for the solution of discrete problems originating from multi-group radiation diffusion equations. We firstly investigate the performances of the most widely used preconditioners (ILU(k) and AMG) and their combinations (Bco and Bco), and provide drawbacks on their feasibilities. Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing the features suitable for AMG using more detailed measurements on multiscale nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present an adaptive combined preconditioner Bcoα involving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that Bcoα-GMRES holds the best robustness and efficiency. At last, we analyze the convergence of GMRES with combined preconditioning which not only provides a persuasive support for our proposed algorithms, but also updates the existing estimation theory on condition numbers of combined preconditioned systems.

scholarly journals A consistent approach to solving the radiation diffusion equation

2003 ◽  
Vol 10 (5) ◽  
pp. 1829-1845 ◽  
Author(s):  
James H. Hammer ◽  
Mordecai D. Rosen
Keyword(s):  
Diffusion Equation ◽  
Radiation Diffusion ◽  
Consistent Approach

Correlations for Interaction Layer Growth in U-Mo/Al Dispersion Fuels

2017 ◽  
Vol 375 ◽  
pp. 29-39
Author(s):  
Boris A. Tarasov ◽  
Stepan N. Nikitin ◽  
Dmitry P. Shornikov ◽  
Maria S. Tarasova ◽  
Igor I. Konovalov
Keyword(s):  
Growth Rate ◽  
Growth Process ◽  
Aluminum Matrix ◽  
Layer Growth ◽  
Radiation Diffusion ◽  
Fission Rate ◽  
Interaction Layer ◽  
The Matrix ◽  
Mechanism And Kinetics ◽  
Kinetics Of

Paper presents the results of the growth rate of the interaction layer of uranium-molybdenum dispersed fuel in aluminum matrix and influence of silicon alloying on it. The growth process of amorphous interaction layer depends on the radiation diffusion which is proportional to the fission rate in the power of 1⁄4. The alloying of the matrix by silicon does not lead to a change in the mechanism and kinetics of the interaction layer growth, but only slows it down.

Nonlinear elimination of magnetoresistance divergences due to Landau quantization

1987 ◽  
Vol 35 (12) ◽  
pp. 6438-6441 ◽  
Author(s):  
N. J. M. Horing ◽  
H. L. Cui ◽  
X. L. Lei
Keyword(s):  
Nonlinear Elimination

scholarly journals Invariant Imbedding and the Radiation Transfer in a Plane-Parallel Inhomogeneous Atmosphere

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Arthur G. Nikoghossian
Keyword(s):  
High Speed ◽  
Radiation Transfer ◽  
Energy Sources ◽  
Invariant Imbedding ◽  
Distributed Energy ◽  
Initial Value ◽  
Radiation Diffusion ◽  
Inhomogeneous Atmosphere ◽  
Plane Parallel ◽  
Transfer Problems

The invariant imbedding technique is applied to the problems of radiation transfer in a plane-parallel inhomogeneous atmosphere. All the parameters which describe the elementary event of scattering and the distribution of the energy sources are allowed to vary with depth. Mathematically, the considered standard problems of the theory are reduced to initial-value problems which are better adapted to capabilities of the modern high speed computers. The reflectance of an atmosphere is shown to play a prominent role in describing the diffusion process since all the other characteristics of the radiation field are expressed through it. Three transfer problems frequently encountered in astrophysical applications are discussed: the radiation diffusion in the source-free medium, in a medium with arbitrarily distributed energy sources, as well as the problem of finding the statistical mean quantities, characteristics of the multiple scattering in the atmosphere.

Quartz-Fiber Thermal Insulation: Infrared Radiative Properties and Calculation of Radiative-Conductive Heat Transfer

1996 ◽  
Vol 118 (2) ◽  
pp. 408-414 ◽  
Author(s):  
L. A. Dombrovsky
Keyword(s):  
Heat Transfer ◽  
Disperse Material ◽  
Conductive Heat Transfer ◽  
Radiative Properties ◽  
Conductive Heat ◽  
Radiation Diffusion ◽  
Fiber Thermal Insulation ◽  
Good Agreement ◽  
Scattering And Radiation

Calculations of absorption, transport scattering, and radiation diffusion coefficients for a highly porous material of quartz fibers are performed by use of rigorous scattering theory for arbitrarily oriented cylinders. New results concerning resonance absorption in the semitransparency region and intensive “scattering by absorption” at refractive index n ≈ 1 in the opacity region are obtained. Numerical results for the radiation diffusion coefficient from a theoretical model without taking into account both dependent scattering and interference effects are in a good agreement with the experimental data for isotropic fibrous material of density 144 kg/m3. Calculations allow us to give practical proposals to simplify the determination of optical properties of poly disperse material with randomly oriented fibers. Some results on the radiative–conductive heat transfer in the material considered are presented. The radiation transfer is described in the P1 approximation. A two-band spectral model with bands corresponding to semitransparency and opacity regions is proposed. Applicability of a modified radiative conduction approximation both to transient and to steady-state calculations is discussed.

Self-similar solutions for a nonlinear radiation diffusion equation

2006 ◽  
Vol 13 (9) ◽  
pp. 092703 ◽  
Author(s):  
Josselin Garnier ◽  
Guy Malinié ◽  
Yves Saillard ◽  
Catherine Cherfils-Clérouin
Keyword(s):  
Diffusion Equation ◽  
Radiation Diffusion ◽  
Nonlinear Radiation ◽  
Self Similar ◽  
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