Discrete-Analytical Difference Scheme for Solving the Nonstationary Particle Transport Equation by the Splitting Method View Full Text


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Article Info

DATE

2022-07

AUTHORS

N. Ya. Moiseev, V. M. Shmakov

ABSTRACT

A discrete-analytical difference scheme is presented for solving the nonstationary kinetic particle (neutron) transport equation in the multigroup isotropic approximation by applying the splitting method. A feature of the scheme is that the solution of the transport equation in the multigroup model is reduced to solving equations in the one-group model. The efficiency of the scheme is ensured by computing the collision integral with the use of analytical solutions of ordinary differential equations describing the evolution of neutrons arriving at the group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g$$\end{document} from all groups \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g{\kern 1pt} '$$\end{document}. Solutions of the equations are found without using iteration with respect to the collision integral or matrix inversion. The solution method can naturally be generalized to problems in multidimensional spaces and can be parallelized. More... »

PAGES

1171-1179

References to SciGraph publications

  • 2011-05-20. High-order accurate implicit running schemes in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
  • 2008-07-18. Arbitrary-order difference schemes for solving linear advection equations with constant coefficients by the Godunov method with antidiffusion in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
  • 2016-08. Modified splitting method for solving the nonstationary kinetic particle transport equation in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1134/s0965542522070077

    DOI

    http://dx.doi.org/10.1134/s0965542522070077

    DIMENSIONS

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