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3 edition of Numerical solutions of the neutron transport equation found in the catalog.

Numerical solutions of the neutron transport equation

David Roy Skeen

Numerical solutions of the neutron transport equation

by David Roy Skeen

  • 377 Want to read
  • 35 Currently reading

Published .
Written in English

    Subjects:
  • Nuclear fuels -- Estimates.,
  • Nuclear reactors -- Refueling.

  • Edition Notes

    Statementby David Roy Skeen.
    The Physical Object
    Pagination90 leaves, bound :
    Number of Pages90
    ID Numbers
    Open LibraryOL14351277M

    Week 3 – Neutron Transport Equation 2 - 9 H;|Violeta 1 – Word\web\Neutron Transport We now set out to calculate the rate of fission at all locations inside a fission reactor. To do this we must first solve for the space-energy-time distribution of the neutrons that cause fission.   Especially the chapter Characteristic ray solutions of the transport equation by H.D. Brough and C.T. Chudley. Google Scholar Martin Becker, Jeffery Lewins (Editors), Advances in nuclear science and technology Vol , Academic Press, Londres, UK, ISBN 0 Author: Serge Marguet.

    The derivation of diffusion equation is based on Fick’s law which is derived under many diffusion equation can, therefore, not be exact or valid at places with strongly differing diffusion coefficients or in strongly absorbing media. This implies that the diffusion theory may show deviations from a more accurate solution of the transport equation in the proximity of external.   On bounded solutions of transport equation solved with a spectral method Olga Martin Numerical Methods for Partial Differential Equations, , Vol Number 4, Page Cited by: 7.

    A Review of Neutron Transport Approximations R. Sanchez and N. 1. McCormick University of Washington, Department of Nuclear Engineering Seattle, Washington Received Febru Numerical methods for solving the integrodifferential, integral, and surface-integral forms of the neutron transport equation are reviewed. We study the convergence of the discrete ordinates method in the numerical solution of the transport equation for slab geometry. In particular, the combined effect of spatial and angular approximat Cited by:


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Numerical solutions of the neutron transport equation by David Roy Skeen Download PDF EPUB FB2

Abstract. This book presents a numerical analysis of neutron transport theory. Topics considered include the kinetic reactor equation, adjoint equations, the multigroup kinetic reactor equations, the one-group kinetic equation, solution of one-group problems in the transport theory, the method of spherical harmonics, Galerkin's method, the finite-difference equations of the spherical-harmonic.

@article{osti_, title = {Computational methods of neutron transport}, author = {Lewis, E.E. and Miller, W.F.}, abstractNote = {This books presents a balanced overview of the major methods currently available for obtaining numerical solutions in neutron and gamma ray transport.

It focuses on methods particularly suited to the complex problems encountered in the analysis of reactors. Numerical solution of the neutron transport equation and the source of neutrons deep within the interior have the form's i 7V (x P) _ ~ Zo + ex/Z" () where the constant B is chosen such that f o,qp(0, Cited by: 4.

This chapter presents the numerical analysis of the neutron transport equation. It reviews some regularity results for solutions of the transport equation, and discusses some numerical methods for solving the equation.

The solutions of the transport equation display singularities, even in the simplest : R.B. Kellogg. exact solutions to model problems of elliptic, hyperbolic, and parabolic type.

Next, we review the basic steps involved in the design of numerical approximations and the main criteria that a reliable algorithm should satisfy. The chapter concludes with an outline of the rationale behind the scope and structure of the present book.

Modern solutions use either discrete-ordinates or Monte Carlo methods, or even a hybrid of both. Neutron transport equation. The neutron transport equation is a balance statement that conserves neutrons. Each term represents a gain or a loss of a neutron, and the balance, in essence, claims that neutrons gained equals neutrons lost.

Formal solutions are numerically “cheap” and we don’t need an explicit expression for in order to obtain the formal solution. Problems: ity of numerical integration (relatively easy to beat down) 2. S depends on J Lecture 3 Numerical Solutions to the Transport Equation.

Triangular Mesh Method for the Neutron Transport Equation,” Los Alamos Report, () by W H Reed, T Hill Add To MetaCart Numerical results for the nonlinear Euler equations up to 6th order of accuracy in space and time are provided as well. Mesh refinement studies for simple problems with analytic solutions demonstrate that the.

The neutron transport equation is an integro-differential equation which describes the distribution of neutron angular flux (Ψ) as a function of space (r), angle (Ω), energy (E) and time (t) in. The subject of this work is computational modeling of neutron trans-port relevant to economical and safe operation of nuclear facilities.

The general mathematical model of neutron transport is provided by the linear Boltzmann’s transport equation and the thesis begins with its precise mathematical formulation and presentation of known con-File Size: 7MB. One of the most difficult problems in time-dependent neutron transport solution concerns the generation of negative flux due to a great opacity provided by an additional term summed to total neutron cross section that arises when the transport equation is discretized in time, as we will see ahead.

The numerical solution developed here employs. A Numerical Solution of the Time-Dependent Neutron Transport Equation Using the Characteristic Method. Applications to ICF and to Hybrid Fission-Fusion Systems Article (PDF Available) April. A difference form of the Boltzmann equation is derived as the final expression for machine computation.

Comparisons are given of the numerical solutions with an analytical solution for a constant source distribution, and with NIOBE calculations and experimental spectra for neutron transport in water, with good agreement obtained between by: 7. Abstract. A central problem in the safety analysis of nuclear reactors is the determination of the neutron distribution in the reactor core.

This is usually done by treating the neutron motion as a diffusion process and solving the diffusion equation : Werner Schmid, Frank Wagner. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Numerical Methods in the Theory of Neutron Transport Revised, Subsequent Edition by G. Marchuk (Author)Cited by: [10] Kaper, H.G., G.K. Leaf and A.J. Lindeman "Application of finite element techniques for the numerical solution of the neutron transport and diffusion equations" Proc.

Conf. on Transport Theory, 2nd Conf.Los Alamos ().Cited by: Key Words- Neutron diffusion, Radial basis function collocation, Multiquadric 1. INTRODUCTION Numerical solution of the neutron diffusion equation has been done by many numerical methods such as the finite difference, finite element and boundary element methods.

These are all mesh-based methods in which the nodes that discretize theFile Size: KB. The numerical solution to the one-group time-dependent neutron transport equation in infinite plane, spherical and cylindrical geometries is obtained via an expansion in Legendre by: Abstract: Stochastic difference equations and a stochastic partial differential equation (SPDE) are simultaneously derived for the time-dependent neutron angular density in a general three-dimensional medium where the neutron angular density is a function of position, direction, energy, and time.

Special cases of the equations are given such as transport in one-dimensional plane geometry with Author: Edward J. Allen. SOLUTION OF THE NEUTRON TRANSPORT EQUATION JAMES A. RATHKOPF* and WILLIAM R. MARTIN Department of Nuclear Engineering, The University of Michigan, Ann Arbor, Michigan, U.S.A.

Abstract--The finite element response matrix method has been applied to .The developers of computer codes involving neutron transport theory for nuclear engineering applications seldom apply analytical benchmarking strategies to ensure the quality of their programs.

A major reason for this is the lack of analytical benchmarks and their documentation in the literature.T1 - Second-order neutron transport methods. AU - Lewis, Elmer E. PY - /12/1.

Y1 - /12/1. N2 - Among the approaches to obtaining numerical solutions for neutral particle transport problems, those classified as second-order or even-parity methods have found increased use in recent by: 9.