Spherical Harmonic Solutions of the Neutron Transport Equation from Discrete Ordinate Codes

Reed, W.H.

doi:10.13182/nse72-a22523

Cited by 36 publications

(12 citation statements)

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“…Diffusion [15,12,14,11,9,43,25,38,6,5,31,35,44,46,27,37,1,42,41,28] 3. Spherical Harmonics (P N ) [7,10,40,13] 4. Implicit Monte Carlo (IMC) [17,22] The diffusion equation is very easy to solve but is inaccurate in optically thin regions and where the gradient of the energy density is large.…”

Section: The Approximationsmentioning

confidence: 99%

“…The discrete ordinates approximation in more than one spatial dimension has a well-known defect called ray effects [32,34,7]. Due to the discrete nature of the angular approximation, particles do not reach regions where they otherwise would, sometimes producing large spatial oscillations in the energy density E. There have been some attempts to eliminate ray effects by introducing extra terms into the equations that act like extra scattering [4,40,24].…”

Section: Discrete Ordinatesmentioning

confidence: 99%

“…2, must also approximate the natural boundary conditions described in Eqs. [40][41][42][43][44]. In discrete ordinates, each of the boundary conditions is averaged over an angular range and assigned to the corresponding beam.…”

Section: A Boundary Conditionsmentioning

confidence: 99%

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Forms of Approximate Radiation Transport

Brunner

2002

126

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Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.4

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Section: The Approximationsmentioning

confidence: 99%

Section: Discrete Ordinatesmentioning

confidence: 99%

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Forms of Approximate Radiation Transport

Brunner

2002

126

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“…Another steady state problem used to test the diffusion correction is a modified version of Reed's problem [28]. The problem was modified to make the diffusive region in the problem optically thick.…”

Section: Steady State Problemsmentioning

confidence: 99%

Advances in radiation modeling in ALEGRA :a final report for LDRD-67120, efficient implicit mulitgroup radiation calculations.

Mehlhorn¹,

Kurecka

McClarren

et al. 2005

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The original LDRD proposal was to use a nonlinear diffusion solver to compute estimates for the material temperature that could then be used in a Implicit Monte Carlo (IMC) calculation. At the end of the first year of the project, it was determined that this was not going to be effective, partially due to the concept, and partially due to the fact that the radiation diffusion package was not as efficient as it could be.The second, and final year, of the project focused on improving the robustness and computational efficiency of the radiation diffusion package in ALEGRA. To this end, several new multigroup diffusion methods have been developed and implemented in ALEGRA. While these methods have been implemented, their effectiveness of reducing overall simulation run time has not been fully tested.Additionally a comprehensive suite of verification problems has been developed for the diffusion package to ensure that it has been implemented correctly. This process took considerable time, but exposed significant bugs in both the previous and new diffusion packages, the linear solve packages, and even the NEVADA Framework's parser.In order to manage this large suite of problem, a new tool called Tampa has been developed. It is a general tool for automating the process of running and analyzing many simulations.Ryan McClarren, at the University of Michigan has been developing a Spherical Harmonics capability for unstructured meshes. While still in the early phases of development, this promises to bridge the gap in accuracy between a full transport solution using IMC and the diffusion approximation. 4 AcknowledgmentThe Trilinos team, especially Mike Heroux, provided a lot of support so that the advanced features of Trilinos could be used effectively in order to get robust, efficient code. 5 6

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“…The renewed interest has been expressed in transforming the discrete ordinates equations (5'jy) to spherical harmonics equa tions {P]\f -i) [11][12][13].…”

Section: (3) Discrete Ordinates (Sj^) Methodsmentioning

confidence: 99%

The SK(N) approximation: a new method for solving integral transport equations

Altaç

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Altac, Zekeriya, "The SK(N) approximation: a new method for solving integral transport equations " (1989 INFORMATION TO USERSThe most advanced technology has been used to photo graph and reproduce this manuscript from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer, jirinter.The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction.In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.Oversize materials (e.g., maps, drawings, charts) are re produced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. These are also available as one exposure on a standard 35mm slide or as a 17" x 23" black and white photographic print for an additional charge.

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Spherical Harmonic Solutions of the Neutron Transport Equation from Discrete Ordinate Codes

Cited by 36 publications

References 0 publications

Forms of Approximate Radiation Transport

Forms of Approximate Radiation Transport

Advances in radiation modeling in ALEGRA :a final report for LDRD-67120, efficient implicit mulitgroup radiation calculations.

The SK(N) approximation: a new method for solving integral transport equations

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