Converged accelerated finite difference scheme for the multigroup neutron diffusion equation

Nicholas Terranova, Domiziano Mostacci, Barry D Ganapol

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

Abstract

Computer codes involving neutron transport theory for nuclear engineering applications always require verification to assess improvement. Generally, analytical and semi-analytical benchmarks are desirable, since they are capable of high precision solutions to provide accurate standards of comparison. However, these benchmarks often involve relatively simple problems, usually assuming a certain degree of abstract modeling. In the present work, we show how semi-analytical equivalent benchmarks can be numerically generated using convergence acceleration. Specifically, we investigate the error behavior of a 1D spatial finite difference scheme for the multigroup (MG) steady-state neutron diffusion equation in plane geometry. Since solutions depending on subsequent discretization can be envisioned as terms of an infinite sequence converging to the true solution, extrapolation methods can accelerate an iterative process to obtain the limit before numerical instability sets in. The obtained results have been compared to the analytical solution to the 1D multigroup diffusion equation when available, using FORTRAN as the computational language. Finally, a slowing down problem has been solved using a cascading source update, showing how a finite difference scheme performs for ultra-fine groups (104 groups) in a reasonable computational time using convergence acceleration.

Original languageEnglish (US)
Title of host publicationInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013
Pages2088-2102
Number of pages15
Volume3
StatePublished - 2013
EventInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013 - Sun Valley, ID, United States
Duration: May 5 2013May 9 2013

Other

OtherInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013
CountryUnited States
CitySun Valley, ID
Period5/5/135/9/13

Fingerprint

Neutron
Finite Difference Scheme
Diffusion equation
Convergence Acceleration
Neutrons
Benchmark
D.3.2 [Programming Languages]: Language Classifications - Fortran
Nuclear engineering
Neutron Transport
Extrapolation Method
Transport Theory
Numerical Instability
Iterative Process
Engineering Application
Extrapolation
Accelerate
Analytical Solution
Update
Discretization
Geometry

Keywords

  • Convergence acceleration
  • Extrapolation methods
  • Multigroup
  • Neutron diffusion equation
  • Ultra-fine group

ASJC Scopus subject areas

  • Nuclear Energy and Engineering
  • Applied Mathematics

Cite this

Terranova, N., Mostacci, D., & Ganapol, B. D. (2013). Converged accelerated finite difference scheme for the multigroup neutron diffusion equation. In International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013 (Vol. 3, pp. 2088-2102)

Converged accelerated finite difference scheme for the multigroup neutron diffusion equation. / Terranova, Nicholas; Mostacci, Domiziano; Ganapol, Barry D.

International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013. Vol. 3 2013. p. 2088-2102.

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

Terranova, N, Mostacci, D & Ganapol, BD 2013, Converged accelerated finite difference scheme for the multigroup neutron diffusion equation. in International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013. vol. 3, pp. 2088-2102, International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013, Sun Valley, ID, United States, 5/5/13.
Terranova N, Mostacci D, Ganapol BD. Converged accelerated finite difference scheme for the multigroup neutron diffusion equation. In International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013. Vol. 3. 2013. p. 2088-2102
Terranova, Nicholas ; Mostacci, Domiziano ; Ganapol, Barry D. / Converged accelerated finite difference scheme for the multigroup neutron diffusion equation. International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013. Vol. 3 2013. pp. 2088-2102
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