Development of a Nodal Method for the Solution of the Neutron Diffusion Equation in General Cylindrical Geometry

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The usual strategy for solving the neutron diffusion equation in two or three dimensions by nodal methods is to reduce the multidimensional partial differential equation to a set of ordinary differential equations (ODEs) in the separate spatial coordinates. This reduction is accomplished by “transverse integration” of the equation.1 For example, in three-dimensional Cartesian coordinates, the three-dimensional equation is first integrated over x and y to obtain an ODE in z, then over x and z to obtain an ODE in y, and finally over y and z to obtain an ODE in x. Then the ODEs are solved to obtain ... continued below

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Ougouag, Abderrafi Mohammed-El-Ami & Terry, William Knox April 1, 2002.

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Description

The usual strategy for solving the neutron diffusion equation in two or three dimensions by nodal methods is to reduce the multidimensional partial differential equation to a set of ordinary differential equations (ODEs) in the separate spatial coordinates. This reduction is accomplished by “transverse integration” of the equation.1 For example, in three-dimensional Cartesian coordinates, the three-dimensional equation is first integrated over x and y to obtain an ODE in z, then over x and z to obtain an ODE in y, and finally over y and z to obtain an ODE in x. Then the ODEs are solved to obtain onedimensional solutions for the neutron fluxes averaged over the other two dimensions. These solutions are found in regions (“nodes”) small enough for the material properties and cross sections in them to be adequately represented by average values. Because the solution in each node is an exact analytical solution, the nodes can be much larger than the mesh elements used in finite-difference solutions. Then the solutions in the different nodes are coupled by applying interface conditions, ultimately fixing the solutions to the external boundary conditions.

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  • Report No.: INEEL/EXT-02-00489
  • Grant Number: DE-AC07-99ID-13727
  • DOI: 10.2172/910654 | External Link
  • Office of Scientific & Technical Information Report Number: 910654
  • Archival Resource Key: ark:/67531/metadc890117

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  • April 1, 2002

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  • Sept. 22, 2016, 2:13 a.m.

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  • Nov. 7, 2016, 7:37 p.m.

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Ougouag, Abderrafi Mohammed-El-Ami & Terry, William Knox. Development of a Nodal Method for the Solution of the Neutron Diffusion Equation in General Cylindrical Geometry, report, April 1, 2002; [Idaho Falls, Idaho]. (digital.library.unt.edu/ark:/67531/metadc890117/: accessed August 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.