Radiation Physics and Engineering
A peer-reviewed journal published by K. N. Toosi University of Technology

‎Investigation of the use of momentum and Galerkin weighting functions in high-order Nodal expansion method to solve the neutron diffusion equation

Document Type : Research Article

Authors

Ali Kolali
ِDavod Naghavi Dizaji
Naser Vosoughi

Department of Energy Engineering‎, ‎Sharif University of Technology‎, ‎P.O‎. ‎Box 14565-1114‎, ‎Tehran‎, ‎Iran

https://doi.org/10.22034/rpe.2022.337683.1078
Abstract
In this study, after discretization of the neutron diffusion equation and adjoint with high-order nodal expansion method in two dimensions and two energy groups, calculations with Momentum and Galerkin weighting functions for rectangular geometry (BIBLIS-2D) and hexagonal geometry (IAEA-2D) reactors are performed. The mean of relative power error for Momentum and Galerkin weighting functions was calculated in BIBLIS-2D reactor 0.42% and 0.62%, respectively, and for IAEA-2D reactor 4.96% and 3.52%, respectively. Regarding the results, it was concluded that in order to increase accuracy with the acceptable time of computing (4 Seconds for rectangular geometry and 28 seconds for hexagonal geometry with Intel® Core™ i7-4510U Processor), the Momentum weighting function for rectangular geometry and the Galerkin weighting function for hexagonal geometry can be used to discretize equations without reducing the node size. Therefore, to increase the accuracy while maintaining the speed of calculations, without reducing the size of nodes, the appropriate weighting function can be used in discretization, which can be very useful in performing calculations of different transients.

Highlights

  • Development of high-speed and accurate steady-state neutronic simulator using the high-order nodal expansion method.
  • Use of polynomials with Momentum and Galerkin weighting functions in discretization of neutron diffusion equation.
  • These weighting functions for rectangular and hexagonal geometries can be used to discretize equations.
  • It was concluded that accuracy increases within the acceptable time of computing

Keywords

Simulator
Adjoint calculation
Diffusion equation
Rectangular geometry
Hexagonal Geometry
HACNEM
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Radiation Physics and Engineering
Volume 3, Issue 3
Summer 2022
Pages 39-45

  • Receive Date 15 April 2022
  • Revise Date 08 June 2022
  • Accept Date 11 June 2022

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