Numerical Formulation And Solution Of Neutron Transport Problems
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Numerical Formulation And Solution Of Neutron Transport Problems
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Author : Bengt G. Carlson
language : en
Publisher:
Release Date : 1964
Numerical Formulation And Solution Of Neutron Transport Problems written by Bengt G. Carlson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Neutron transport theory categories.
Numerical Solution Of Transient And Steady State Neutron Transport Problems
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Author : Bengt G. Carlson
language : en
Publisher:
Release Date : 1959
Numerical Solution Of Transient And Steady State Neutron Transport Problems written by Bengt G. Carlson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Neutron transport theory categories.
The Dsn And Tdc Neutron Transport Codes
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Author : B. Carlson
language : en
Publisher:
Release Date : 1960
The Dsn And Tdc Neutron Transport Codes written by B. Carlson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Neutron transport theory categories.
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.
Numerical Methods In The Theory Of Neutron Transport
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Author : Guriĭ Ivanovich Marchuk
language : en
Publisher: Harwood Academic Publishers
Release Date : 1986
Numerical Methods In The Theory Of Neutron Transport written by Guriĭ Ivanovich Marchuk and has been published by Harwood Academic Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Neutron transport theory categories.
Numerical Solution Of Transient And Steady State Neutron Transport Problems
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Author :
language : en
Publisher:
Release Date : 1959
Numerical Solution Of Transient And Steady State Neutron Transport Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with categories.
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).
Novel Parallel Numerical Methods For Radiation Neutron Transport
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Author :
language : en
Publisher:
Release Date : 2001
Novel Parallel Numerical Methods For Radiation Neutron Transport written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both.
Development Of Advanced Numerical Methods For Solving Neutron Transport Problems
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Author : Tseelmaa Byambaakhuu
language : en
Publisher:
Release Date : 2021
Development Of Advanced Numerical Methods For Solving Neutron Transport Problems written by Tseelmaa Byambaakhuu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Neutron transport theory categories.
Instabilities and oscillations may occur in the solution due to sharp boundary and/or interior layers when the mesh is not fine enough around the sharp layers. Unlike the convection-diffusion problem where the singular perturbation parameter is known, the mesh transition point for hyperbolic type neutron transport problems must be determined. To address this challenge, we have analytically developed a formula to calculate this parameter. The mathematical expression calculates the boundary/interior layer thickness based on the 1D analytical solution. Numerical results for the diamond difference (DD) and discontinuous Galerkin (DG) methods are presented to improve the accuracy, stability, and efficiency of the Shishkin mesh.
Neutron Transport
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Author : Ramadan M. Kuridan
language : en
Publisher: Springer Nature
Release Date : 2023-10-28
Neutron Transport written by Ramadan M. Kuridan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-28 with Science categories.
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.
Deterministic Numerical Methods For Unstructured Mesh Neutron Transport Calculation
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Author : Liangzhi Cao
language : en
Publisher: Woodhead Publishing
Release Date : 2020-08-30
Deterministic Numerical Methods For Unstructured Mesh Neutron Transport Calculation written by Liangzhi Cao and has been published by Woodhead Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-30 with Technology & Engineering categories.
Deterministic Numerical Methods for Unstructured-Mesh Neutron Transport Calculation presents the latest deterministic numerical methods for neutron transport equations (NTEs) with complex geometry, which are of great demand in recent years due to the rapid development of advanced nuclear reactor concepts and high-performance computational technologies. This book covers the wellknown methods proposed and used in recent years, not only theoretical modeling but also numerical results. This book provides readers with a very thorough understanding of unstructured neutron transport calculations and enables them to develop their own computational codes. The fundamentals, numerical discretization methods, algorithms, and numerical results are discussed. Researchers and engineers from utilities and research institutes are provided with examples on how to model an advanced nuclear reactor, which they can then apply to their own research projects and lab settings. Combines the theoretical models with numerical methods and results in one complete resource Presents the latest progress on the topic in an easy-to-navigate format
New Splitting Iterative Methods For Solving Multidimensional Neutron Transport Equations
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Author : Jacques Tagoudjeu
language : en
Publisher: Universal-Publishers
Release Date : 2011-04
New Splitting Iterative Methods For Solving Multidimensional Neutron Transport Equations written by Jacques Tagoudjeu and has been published by Universal-Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04 with Mathematics categories.
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.
