High order finite difference approximations to the one-group neutron diffusion equation in 1D heterogeneous media part I: Theory in plane media

Barry D. Ganapol, David W. Nigg

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

1 Scopus citations

Abstract

Verification that a numerical method performs as intended is an integral part of code development. Semi-analytical benchmarks enable one such verification modality. Unfortunately, a semi-analytical benchmark requires some degree of analytical forethought and treats only relatively idealized cases making it of limited diagnostic value. In the first part of our investigation (Part I), we establish the theory of a straightforward finite difference scheme for the 1D, monoenergetic neutron diffusion equation in plane media. We also demonstrate an analytically enhanced version that leads directly to the analytical solution. The second part of our presentation (Part II, in these proceedings) is concerned with numerical implementation and application of the finite difference solutions. There, we demonstrate how the numerical schemes themselves provide the semi-analytical benchmark. With the analytical solution known, we therefore have a test for accuracy of the proposed finite difference algorithms designed for high order.

Original languageEnglish (US)
Title of host publicationInternational Conference on the Physics of Reactors 2010, PHYSOR 2010
Pages3244-3266
Number of pages23
StatePublished - Dec 1 2010
EventInternational Conference on the Physics of Reactors 2010, PHYSOR 2010 - Pittsburgh, PA, United States
Duration: May 9 2010May 14 2010

Publication series

NameInternational Conference on the Physics of Reactors 2010, PHYSOR 2010
Volume4

Other

OtherInternational Conference on the Physics of Reactors 2010, PHYSOR 2010
CountryUnited States
CityPittsburgh, PA
Period5/9/105/14/10

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Keywords

  • Analytical
  • Diffusion theory
  • Finite difference
  • High order
  • Monoenergetic

ASJC Scopus subject areas

  • Nuclear Energy and Engineering
  • Nuclear and High Energy Physics

Cite this

Ganapol, B. D., & Nigg, D. W. (2010). High order finite difference approximations to the one-group neutron diffusion equation in 1D heterogeneous media part I: Theory in plane media. In International Conference on the Physics of Reactors 2010, PHYSOR 2010 (pp. 3244-3266). (International Conference on the Physics of Reactors 2010, PHYSOR 2010; Vol. 4).