Numerical Formulation and Solution of Neutron Transport Problems PDF Download

Author: Bengt G. Carlson
Publisher:
ISBN:
Category : Neutron transport theory
Languages : en
Pages : 54

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Author: Bengt G. Carlson
Publisher:
ISBN:
Category : Neutron transport theory
Languages : en
Pages : 34

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Author: Guriĭ Ivanovich Marchuk
Publisher: Harwood Academic Publishers
ISBN:
Category : Neutron transport theory
Languages : en
Pages : 632

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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :

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A general numerical procedure, called the discrete S/sub n/ method, for solving the neutron transport equation is described. The main topics relate to the derivation of suitable difference equations, and to the problem of solving these, while maintaining generality, accuracy, and reasonable computing speed. A few comparisons with other methods are made. (auth).

Author: B. Carlson
Publisher:
ISBN:
Category : Neutron transport theory
Languages : en
Pages : 38

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Book Description
This report describes two reactor codes, one for the one-dimensional geometries (DSN) and the other for the finite cylindrical case (TDC), based on the transport difference equations and calculation methods developed in "Numerical Solutions of Transient and Steady State Neutron Transport Problems" (LA-2260). Appendices I and II, which contain the actual machine codes, have been separated from the descriptive part of the report to make it easier for the user to study the material and apply it to problems.

Author: Ramadan M. Kuridan
Publisher: Springer Nature
ISBN: 3031269322
Category : Science
Languages : en
Pages : 284

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Book Description
This textbook provides a thorough explanation of the physical concepts and presents the general theory of different forms through approximations of the neutron transport processes in nuclear reactors and emphasize the numerical computing methods that lead to the prediction of neutron behavior. Detailed derivations and thorough discussions are the prominent features of this book unlike the brevity and conciseness which are the characteristic of most available textbooks on the subject where students find them difficult to follow. This conclusion has been reached from the experience gained through decades of teaching. The topics covered in this book are suitable for senior undergraduate and graduate students in the fields of nuclear engineering and physics. Other engineering and science students may find the construction and methodology of tackling problems as presented in this book appealing from which they can benefit in solving other problems numerically. The book provides access to a one dimensional, two energy group neutron diffusion program including a user manual, examples, and test problems for student practice. An option of a Matlab user interface is also available.

Author: Herbert Bishop Keller
Publisher:
ISBN:
Category : Elastic scattering
Languages : en
Pages : 48

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A procedure for the direct numerical integration of the steady-state, elastic scattering neutron transport equation is presented.

Author: Bruce Carl Wilson
Publisher:
ISBN:
Category : Neutron transport theory
Languages : en
Pages : 306

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Author: Jacques Tagoudjeu
Publisher: Universal-Publishers
ISBN: 1599423960
Category : Mathematics
Languages : en
Pages : 161

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Book Description
This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of Rn (n = 2,3) and in 1-D spherical geometry. We introduce a generic Alternate Direction Implicit (ADI)-like iterative method based on positive definite and m-accretive splitting (PAS) for linear operator equations with operators admitting such splitting. This method converges unconditionally and its SOR acceleration yields convergence results similar to those obtained in presence of finite dimensional systems with matrices possessing the Young property A. The proposed methods are illustrated by a numerical example in which an integro-differential problem of transport theory is considered. In the particular case where the positive definite part of the linear equation operator is self-adjoint, an upper bound for the contraction factor of the iterative method, which depends solely on the spectrum of the self-adjoint part is derived. As such, this method has been successfully applied to the neutron transport equation in slab and 2-D cartesian geometry and in 1-D spherical geometry. The self-adjoint and m-accretive splitting leads to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of minimal residual and preconditioned minimal residual algorithms using Gauss-Seidel, symmetric Gauss-Seidel and polynomial preconditioning are then applied to solve the matrix operator equation. Theoretical analysis shows that the methods converge unconditionally and upper bounds of the rate of residual decreasing which depend solely on the spectrum of the self-adjoint part of the operator are derived. The convergence of theses solvers is illustrated numerically on a sample neutron transport problem in 2-D geometry. Various test cases, including pure scattering and optically thick domains are considered.

Author: Perry A. Newman
Publisher:
ISBN:
Category : Case method
Languages : en
Pages : 122

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Book Description
The solution of an initial-value problem in linear transport theory is obtained by using the normal-mode expansion technique of Case. The problem is that of monoenergetic neutrons migrating in a thin slab surrounded by infinitely thick reflectors and the scattering is taken to be isotropic. The results obtained indicate that the reflector may give rise to a branch-cut integral term typical of a semi-infinite medium whereas the central slab may contribute a summation over discrete residue terms. Exact expressions are obtained for these discrete time eigenvalues, and numerical results showing the behavior of real time eigenvalues as a function of the material properties of the slab and reflector are presented. These eigenvalues are finite in number and may disappear into the branch cut or continuum as the material properties are varied; such disappearing eigenvalues correspond to exponentially time-decaying modes. The two largest eigenvalues can be compared with critical dimensions of slabs and spheres, and the numerical values are shown to agree with the critically results of others. In the limit of purely absorbing reflectors or a bare slab, the present solution has the same properties as have been previously reported by others who used the approach of Lehner and Wing.