Méthodes mathématiques en neutronique

Méthodes mathématiques en neutronique
Author: Jacques Planchard
Publisher:
Total Pages: 432
Release: 1995
Genre: Differential equations, Partial
ISBN: 9782212016437

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Computational Methods in Transport

Computational Methods in Transport
Author: Frank Graziani
Publisher: Springer Science & Business Media
Total Pages: 539
Release: 2006-02-17
Genre: Computers
ISBN: 3540281258

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Thereexistawiderangeofapplicationswhereasigni?cantfractionofthe- mentum and energy present in a physical problem is carried by the transport of particles. Depending on the speci?capplication, the particles involved may be photons, neutrons, neutrinos, or charged particles. Regardless of which phenomena is being described, at the heart of each application is the fact that a Boltzmann like transport equation has to be solved. The complexity, and hence expense, involved in solving the transport problem can be understood by realizing that the general solution to the 3D Boltzmann transport equation is in fact really seven dimensional: 3 spatial coordinates, 2 angles, 1 time, and 1 for speed or energy. Low-order appro- mations to the transport equation are frequently used due in part to physical justi?cation but many in cases, simply because a solution to the full tra- port problem is too computationally expensive. An example is the di?usion equation, which e?ectively drops the two angles in phase space by assuming that a linear representation in angle is adequate. Another approximation is the grey approximation, which drops the energy variable by averaging over it. If the grey approximation is applied to the di?usion equation, the expense of solving what amounts to the simplest possible description of transport is roughly equal to the cost of implicit computational ?uid dynamics. It is clear therefore, that for those application areas needing some form of transport, fast, accurate and robust transport algorithms can lead to an increase in overall code performance and a decrease in time to solution.

The Physics of Nuclear Reactors

The Physics of Nuclear Reactors
Author: Serge Marguet
Publisher: Springer
Total Pages: 1462
Release: 2018-02-26
Genre: Science
ISBN: 3319595601

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This comprehensive volume offers readers a progressive and highly detailed introduction to the complex behavior of neutrons in general, and in the context of nuclear power generation. A compendium and handbook for nuclear engineers, a source of teaching material for academic lecturers as well as a graduate text for advanced students and other non-experts wishing to enter this field, it is based on the author’s teaching and research experience and his recognized expertise in nuclear safety. After recapping a number of points in nuclear physics, placing the theoretical notions in their historical context, the book successively reveals the latest quantitative theories concerning: • The slowing-down of neutrons in matter • The charged particles and electromagnetic rays • The calculation scheme, especially the simplification hypothesis • The concept of criticality based on chain reactions • The theory of homogeneous and heterogeneous reactors • The problem of self-shielding • The theory of the nuclear reflector, a subject largely ignored in literature • The computational methods in transport and diffusion theories Complemented by more than 400 bibliographical references, some of which are commented and annotated, and augmented by an appendix on the history of reactor physics at EDF (Electricité De France), this book is the most comprehensive and up-to-date introduction to and reference resource in neutronics and reactor theory.

Schéma de calcul déterministe

Schéma de calcul déterministe
Author: Otman Jai
Publisher: Presses Academiques Francophones
Total Pages: 120
Release: 2020-06-03
Genre:
ISBN: 9783838147567

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La neutronique, ou physique des neutrons est l'analyse et la mise en équation des différents phénomènes gouvernant une population de neutrons. L'un des problèmes les plus importants en neutronique est celui du transport des neutrons dans un réacteur nucléaire, qui est régit par l'équation de transport. C'est une équation trop complexe et en toute généralité, une solution analytique est inimaginable. C'est pour cela que les méthodes numériques s'avèrent nécessaires. L'étude du comportement du neutron qui permet la compréhension des phénomènes de fission et leur maitrise dans un réacteur de puissance ou de recherche. La connaissance des réactions nucléaires est indispensable pour appréhender, par des modélisations physico-mathématiques appropriées, la physique d'un réacteur nucléaire ainsi que l'ensemble des phénomènes nucléaires associés au cycle du combustible. Les données nucléaires sont essentielles au développement et à l'application des sciences et techniques nucléaires. Les données nucléaires de base, qu'elles soient mesurées ou calculées, sont soumises à un processus complexe d'évaluation, de correction et d'analyse avant d'être disponibles pour les applications.

Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications

Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications
Author: Andreas Kling
Publisher: Springer Science & Business Media
Total Pages: 1200
Release: 2014-02-22
Genre: Science
ISBN: 3642182119

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This book focuses on the state of the art of Monte Carlo methods in radiation physics and particle transport simulation and applications. Special attention is paid to algorithm development for modeling, and the analysis of experiments and measurements in a variety of fields.

New Splitting Iterative Methods for Solving Multidimensional Neutron Transport Equations

New Splitting Iterative Methods for Solving Multidimensional Neutron Transport Equations
Author: Jacques Tagoudjeu
Publisher: Universal-Publishers
Total Pages: 161
Release: 2011-04
Genre: Mathematics
ISBN: 1599423960

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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.

ESAIM.

ESAIM.
Author:
Publisher:
Total Pages: 572
Release: 2002
Genre: Mathematical models
ISBN:

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La physique des réacteurs nucléaires (2e ed)

La physique des réacteurs nucléaires (2e ed)
Author: MARGUET Serge
Publisher: Lavoisier
Total Pages: 1344
Release: 2013-10-18
Genre:
ISBN: 2743065400

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La physique des réacteurs nucléaires est le premier ouvrage français conçu pour aborder de façon progressive et détaillée la complexité théorique du comportement des neutrons, en situation sûre ou accidentelle. Fruit de l’expérience pédagogique de l’auteur et de son expertise internationale reconnue en sûreté nucléaire, il est rapidement devenu un ouvrage de référence au sein de la communauté nucléaire française. Après des rappels de physique nucléaire replaçant les notions théoriques dans leur contexte historique, l’auteur expose les théories mathématico-physiques les plus récentes concernant : • le ralentissement des neutrons dans la matière ; • les particules chargées et les rayonnements électromagnétiques ; • les phases de calcul, en soulignant les hypothèses simplificatrices ; • le concept de criticité, lorsque se développe et s’entretient une réaction nucléaire en chaîne ; • le calcul théorique des réacteurs homogènes et hétérogènes ; • les problèmes d’autoprotection ; • les méthodes numériques des 2 approches historiques du traitement des neutrons (transport neutronique et diffusion). Cette 2e édition, revue et augmentée, approfondit certaines notions, notamment le spectre théorique de fission, l’effet des liaisons cristallines, l’effet de l’hétérogénéité du champ de température, l’effet Dancoff, les équations du transport en géométrie dimensionnelle, le calcul du facteur anti-trappe, la méthode des neutrons pulsés, l’effet d’ombre de l’intégrale de résonance, la méthode Feynman-a, le traitement des instrumentations de l’EPR… Complété par plus de 400 références bibliographiques, dont de nombreuses commentées et une annexe replaçant les travaux d’EDF dans le contexte national du développement de l’énergie nucléaire, cet ensemble constitue la référence théorique la plus complète en neutronique. Cet ouvrage est conforme aux enseignements de l’Institut de transfert de technologie d’EDF et sert de référentiel aux enseignements de l’École nationale supérieure d’ingénieurs de Bourges (INSA-Centre Val de Loire). Il a été conçu pour les ingénieurs et techniciens sur sites souhaitant enrichir leur propre expertise, pour les étudiants de 3e cycle et les élèves ingénieurs en sciences énergétiques.

Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations
Author: Vitoriano Ruas
Publisher: John Wiley & Sons
Total Pages: 378
Release: 2016-08-22
Genre: Technology & Engineering
ISBN: 1119111358

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Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.

Mathematical Analysis and Numerical Methods for Science and Technology

Mathematical Analysis and Numerical Methods for Science and Technology
Author: Robert Dautray
Publisher: Springer Science & Business Media
Total Pages: 754
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642580904

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299 G(t), and to obtain the corresponding properties of its Laplace transform (called the resolvent of - A) R(p) = (A + pl)-l , whose existence is linked with the spectrum of A. The functional space framework used will be, for simplicity, a Banach space(3). To summarise, we wish to extend definition (2) for bounded operators A, i.e. G(t) = exp( - tA) , to unbounded operators A over X, where X is now a Banach space. Plan of the Chapter We shall see in this chapter that this enterprise is possible, that it gives us in addition to what is demanded above, some supplementary information in a number of areas: - a new 'explicit' expression of the solution; - the regularity of the solution taking into account some conditions on the given data (u , u1,f etc ... ) with the notion of a strong solution; o - asymptotic properties of the solutions. In order to treat these problems we go through the following stages: in § 1, we shall study the principal properties of operators of semigroups {G(t)} acting in the space X, particularly the existence of an upper exponential bound (in t) of the norm of G(t). In §2, we shall study the functions u E X for which t --+ G(t)u is differentiable.