The analytical solution to the multigroup diffusion equation in one-dimensional plane, cylindrical and spherical geometries

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

By viewing the multigroup diffusion equation in plane, cylindrical and spherical geometries as matrix equations, standard solution techniques for second order ordinary differential equations can be applied to find analytical solutions. By adjusting the boundary conditions appropriately, a solution with the simplicity of the one-group case in the three geometries is found. Diffusion in cylindrical geometry is used as a demonstration of critical and fixed source problems. No special considerations are required when fission is present or not in any region. The solution is new, and, because of its generality, completely eliminates the need for numerical multigroup solutions of the diffusion equation in heterogeneous plane, spherical and cylindrical geometries.

Original languageEnglish (US)
Title of host publicationJoint International Topical Meeting on Mathematics and Computations and Supercomputing in Nuclear Applications, M and C + SNA 2007
StatePublished - Dec 3 2007
EventJoint International Topical Meeting on Mathematics and Computations and Supercomputing in Nuclear Applications, M and C + SNA 2007 - Monterey, CA, United States
Duration: Apr 15 2007Apr 19 2007

Publication series

NameJoint International Topical Meeting on Mathematics and Computations and Supercomputing in Nuclear Applications, M and C + SNA 2007

Other

OtherJoint International Topical Meeting on Mathematics and Computations and Supercomputing in Nuclear Applications, M and C + SNA 2007
CountryUnited States
CityMonterey, CA
Period4/15/074/19/07

    Fingerprint

ASJC Scopus subject areas

  • Mathematics(all)
  • Nuclear and High Energy Physics

Cite this

Ganapol, B. D. (2007). The analytical solution to the multigroup diffusion equation in one-dimensional plane, cylindrical and spherical geometries. In Joint International Topical Meeting on Mathematics and Computations and Supercomputing in Nuclear Applications, M and C + SNA 2007 (Joint International Topical Meeting on Mathematics and Computations and Supercomputing in Nuclear Applications, M and C + SNA 2007).