An Analytic Method for Solving Static Two-group, 1D Neutron Transport Equations

This work presents the analytic solution for neutron transport equations with 1D geometry, two groups of cross sections and two scattering directions. The objectives of the analytic solutions are twofold. Firstly, the results can provide benchmarks to calibrate other approximation methods. Secondly, the method can be applied to develop multigroup SN[1] methods.

In this summary, we first find the general solution form in a homogeneous region. Then, the results are applied to case studies of 1) a homogeneous core and 2) a heterogeneous system with core and reflector. On the case study problems, the numerical results from the analytical solution are also verified by Monte Carlo simulations.

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Work Title An Analytic Method for Solving Static Two-group, 1D Neutron Transport Equations
Access
Open Access
Creators
  1. Jilang Miao
  2. Miaomiao Jin
License CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
Work Type Conference Proceeding
Publication Date November 2022
Publisher Identifier (DOI)
  1. https://doi.org/10.13182/T127-39909
Related URLs
Source
  1. 2022 American Nuclear Society Winter Meeting
Deposited February 24, 2024

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Version 1
published

  • Created
  • Updated
  • Added Creator Jilang Miao
  • Added Creator Miaomiao Jin
  • Added 2A2GAnalytical.pdf
  • Updated Description, Publication Date, License Show Changes
    Description
    • closed form analytical solution of 1D, two-group, two-angle, neutron transport equations
    Publication Date
    • 2022-11
    License
    • https://creativecommons.org/licenses/by-nc-nd/4.0/
  • Published
  • Updated Source, Publisher, Publisher Identifier (DOI), and 2 more Show Changes
    Source
    • 2022 American Nuclear Society Winter Meeting
    Publisher
    • AMERICAN NUCLEAR SOCIETY
    Publisher Identifier (DOI)
    • doi.org/10.13182/T127-39909
    • https://doi.org/10.13182/T127-39909
    Description
    • closed form analytical solution of 1D, two-group, two-angle, neutron transport equations
    • This work presents the analytic solution for neutron transport equations with 1D geometry, two groups of cross sections and two scattering directions. The objectives of the analytic solutions are twofold. Firstly, the results can provide benchmarks to calibrate other approximation methods. Secondly, the method can be applied to develop multigroup SN[1] methods.
    • In this summary, we first find the general solution form in a homogeneous region. Then, the results are applied to case studies of 1) a homogeneous core and 2) a heterogeneous system with core and reflector. On the case study problems, the numerical results from the analytical solution are also verified by Monte Carlo simulations.
    Related URLs
    • https://www.ans.org/meetings/wm2022/session/view-1481/#paper_4226
  • Updated