Numerical Solution of One-Speed One-Dimensional Diffusion Equation based on Finite Difference and Source Iteration

13 Pages Posted: 15 Jul 2020 Last revised: 20 Jul 2020

See all articles by Jinfeng LI

Jinfeng LI

Department of Electrical and Electronic Engineering, Imperial College London; Centre for Electronics Frontiers, Zepler Institute for Photonics and Nanoelectronics, University of Southampton

Date Written: June 22, 2020

Abstract

Numerical methods are in favor to solve the impenetrable diffusion equations for neutron transport in contrast to using the analytical approach. This work applied a finite difference scheme and inverse power iteration to solve the one-group diffusion problem numerically for a one-dimensional slab containing fissile materials and heavy water. Both numerical and analytical solutions were obtained for comparison. MATLAB was employed to perform iterations and the minimum mesh size search. The effect of the initial guess on the accuracy and computational efficiency was investigated. Arguably, there is an appreciable acceleration for convergence by more intuitive initial estimations, as evidenced by the comparative results in the iteration counts decreasing from 799 to 8 by means of a random sampling method in place of the conventional initial guess method based on uniform flux when searching for the minimum size of the mesh necessary to meet the prescriptive accuracy.

Keywords: Computational Neutronics, Diffusion Equation, Finite Difference, Inverse Power Iteration, MATLAB, Neutron Transport, Power Iteration

Suggested Citation

LI, Jinfeng, Numerical Solution of One-Speed One-Dimensional Diffusion Equation based on Finite Difference and Source Iteration (June 22, 2020). Available at SSRN: https://ssrn.com/abstract=3633159 or http://dx.doi.org/10.2139/ssrn.3633159

Jinfeng LI (Contact Author)

Department of Electrical and Electronic Engineering, Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/jinfeng.li

Centre for Electronics Frontiers, Zepler Institute for Photonics and Nanoelectronics, University of Southampton ( email )

University Rd.
Southampton SO17 1BJ, Hampshire SO17 1LP
United Kingdom

HOME PAGE: http://zepler.soton.ac.uk/people/jl4m19

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