Improved Method for Numerically Solving Multi-Group Reactor Equations

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"A method for solving multi-group reactor equations which arise in the diffusion approximation is outlined. Considerable work has been done on this problem at KAPL and ORNL. Their approach is to replace the differential equations by difference equations. Complications arise in this method where more than one slowing down medium is present since the fluxes are discontinuous at the interfaces. The primary purpose of this article is to develop an exact integral expression for the neutron flux which automatically satisfies the boundary conditions. An iterative method for obtaining the fluxes and critical neutron multiplication ratio based upon the above-mentioned integral … continued below

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Lehman, G. W. September 15, 1954.

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"A method for solving multi-group reactor equations which arise in the diffusion approximation is outlined. Considerable work has been done on this problem at KAPL and ORNL. Their approach is to replace the differential equations by difference equations. Complications arise in this method where more than one slowing down medium is present since the fluxes are discontinuous at the interfaces. The primary purpose of this article is to develop an exact integral expression for the neutron flux which automatically satisfies the boundary conditions. An iterative method for obtaining the fluxes and critical neutron multiplication ratio based upon the above-mentioned integral expression is given. The only approximation used in obtaining the fluxes, in addition to the use of multi-group diffusion theory as the basic model, is the use of numerical integration to evaluate the analytic expression. The equations for a two region, two group spherical reactor are given in a form suitable for machine programing. The extension to more than two regions is also considered.

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  • SuDoc Number: Y 3.At 7:22/NAA-SR-1034
  • Report No.: NAA-SR-1034
  • Accession or Local Control No: metadc1250160
  • Archival Resource Key: ark:/67531/metadc1250160

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  • September 15, 1954

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  • Aug. 10, 2021, 7:36 a.m.

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  • March 17, 2022, 10:23 a.m.

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Lehman, G. W. Improved Method for Numerically Solving Multi-Group Reactor Equations, report, September 15, 1954; Washington D.C.. (https://digital.library.unt.edu/ark:/67531/metadc1250160/: accessed April 13, 2026), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.

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