Download or read book New Splitting Iterative Methods for Solving Multidimensional Neutron Transport Equations written by Jacques Tagoudjeu and published by Universal-Publishers. This book was released on 2011-04 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book New Splitting Iterative Methods for Solving Multidimensional Neutron Transport Equations written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis of Projective Iterative Methods for Solving Multidimensional Transport Problems written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The particle transport equation has a wide range of applications: nuclear engineering, astrophysics, atmospheric science, medical physics, microelectronics manufacturing, etc. It is an integro-differential equation with seven independent variables: 3 spatial, 2 angular, energy, and time, which cannot be solved analytically in most of the cases of interest. The way to solve this equation is to discretize it in space, angle, energy, and time. In practical cases, this leads to a huge sparse matrix. Iterative methods should be used even for solving transport problems on the most powerful computers available nowadays. The need to analyze the behavior of these methods is obvious: knowledge about behavior of methods can help us to improve them and avoid their use in cases in which they are not efficient. Also, if we can predict what should happen in specific cases, we can verify and validate transport codes. Analysis of iterative methods' behavior in highly scattering and strong heterogeneous medium is very important from the point of view of solving various radiative and particle transport problems. It became important for solving neutron transport equation in full-core, due to current industry's interest in obtaining very detailed transport solution without homogenization. For these reasons, the main target of this thesis was to analyze the convergence rate of four methods used to solve the steady state transport equation. We were interested in studying behavior of these methods in case of one and two dimensional strong heterogeneous and highly scattering medium with periodic structure, on rectangular grids. In order to understand better these methods, we analyzed them as well in cases of homogeneous and low scattering medium, uniform grids, etc. The main tool that we used is Fourier analysis. Iteration matrix analysis was a secondary tool that we consider. It proved to be restrictive in some cases but provided a good insight of the methods behavior. In several diffcult.
Download or read book Numerical Methods and Techniques Used in the Two dimensional Neutron diffusion Program PDQ 5 written by L. A. Hageman and published by . This book was released on 1963 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods in the Theory of Neutron Transport written by Guriĭ Ivanovich Marchuk and published by Harwood Academic Publishers. This book was released on 1986 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Comparison of Iterative Methods for the Solution of Elliptic Partial Differential Equations Particularly the Neutron Diffusion Equation written by Kevin N. Schwinkendorf and published by . This book was released on 1983 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two new concepts have been explored in solving the neutron diffusion equation in one and two dimensions. At the present time, the diffusion equation is solved using source iterations. These iterations are performed in a mathematical form which has a great deal of physical significance. Specifically, the neutron production term is on the right-hand side, while the absorption and leakage terms are on the left side. In performing a single source iteration, a distribution for the neutron flux is assumed so that the production term can be calculated. This provides a "known" right-hand side. Solving the difference equation for the flux, which corresponds to this assumed source distribution, gives the next estimate for the flux distribution. This type of iteration has the physically significant characteristic of finding directly, for each iteration, a flux which corresponds to an assumed source distribution. In this thesis it was found that by subtracting the absorption term from both sides of the diffusion equation, and performing "source iterations" with both absorption and production terms on the right-hand side (and only the leakage term on the left-hand side), improved convergence rates were attained in many cases. In one neutron energy group, this new idea of putting the absorption term on the right-hand side worked best with only one region, and where reactor dimensions were large compared to the thermal neutron diffusion length (a”L). In small reactors, where a=L, convergence behavior was similar for both forms of iteration. This new idea was also found to work quite well in one-group multiregion problems. However, due to problems with numerics (inherent asymmetric treatment of the scattering terms), the method does not work at all in a multi-energy group formulation. Secondly, in two dimensions, a closed-form solution to a single source iteration has been found. At this time, the standard method of solution for a two-dimensional source iteration is to perform "inner iterations" to approximately solve for the flux that corresponds to an assumed source. The alternative, up until now, was to solve a giant matrix of the order (N2 x N2). This is a sparse matrix, but it has always been considered as highly undesirable to work with a solution (even though it may be closed-form) where the matrix to be solved increases in order roughly as the fourth power of the number of mesh intervals. The new algebraic form for this closed-form solution involves a matrix of order (N x N), not (N2 x N2). The matrix is, however, a full matrix. What is done, essentially, is to solve simultaneously for all the flux values along the vertical centerline of the two-dimensional problem, and then use a reflective boundary condition across the core centerline, and then the difference equation itself (in vector form) as a set of flux-vector generating equations to generate the entire flux field, line by line. In solving for the first flux vector (at the x = o, or z = o, core centerline), the right-hand side of the matrix problem incorporates all of the source values in the entire problem space. The initial inversion of the full (N x N) matrix algebraically guarantees that the (M+1)th flux vector (on the problem space boundary) will go to zero. This matrix method for two-dimensional neutronic analysis was shown to work well in both cartesian and cylindrical coordinates.
Download or read book Deterministic Numerical Methods for Unstructured Mesh Neutron Transport Calculation written by Liangzhi Cao and published by Woodhead Publishing. This book was released on 2020-08-30 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Neutron Transport written by Ramadan M. Kuridan and published by Springer Nature. This book was released on 2023-10-28 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Formulation and Solution of Neutron Transport Problems written by Bengt G. Carlson and published by . This book was released on 1964 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of Transient and Steady state Neutron Transport Problems written by Bengt G. Carlson and published by . This book was released on 1959 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Neutronics of Advanced Nuclear Systems written by Yican Wu and published by Springer. This book was released on 2019-03-19 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic and comprehensive introduction to the neutronics of advanced nuclear systems, covering all key aspects, from the fundamental theories and methodologies to a wide range of advanced nuclear system designs and experiments. It is the first-ever book focusing on the neutronics of advanced nuclear systems in the world. Compared with traditional nuclear systems, advanced nuclear systems are characterized by more complex geometry and nuclear physics, and pose new challenges in terms of neutronics. Based on the achievements and experiences of the author and his team over the past few decades, the book focuses on the neutronics characteristics of advanced nuclear systems and introduces novel neutron transport methodologies for complex systems, high-fidelity calculation software for nuclear design and safety evaluation, and high-intensity neutron source and technologies for neutronics experiments. At the same time, it describes the development of various neutronics designs for advanced nuclear systems, including neutronics design for ITER, CLEAR and FDS series reactors. The book not only summarizes the progress and achievements of the author’s research work, but also highlights the latest advances and investigates the forefront of the field and the road ahead.
Download or read book The Development of New Two dimensional Response Matrix Iterative Strategies with Specific Application to Nodal Neutron Transport Calculations written by Laura Ann Slagter Olvey and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Numerical Integration of the Neutron Transport Equation written by Herbert Bishop Keller and published by . This book was released on 1955 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: A procedure for the direct numerical integration of the steady-state, elastic scattering neutron transport equation is presented.
Download or read book ERDA Energy Research Abstracts written by United States. Energy Research and Development Administration and published by . This book was released on 1977 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book ERDA Energy Research Abstracts written by United States. Energy Research and Development Administration. Technical Information Center and published by . This book was released on 1977 with total page 1682 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Group Explicit Methods for the Numerical Solution of Partial Differential Equations written by David J. Evans and published by CRC Press. This book was released on 1997-05-22 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new class of methods, termed "group explicit methods," is introduced in this text. Their applications to solve parabolic, hyperbolic and elliptic equations are outlined, and the advantages for their implementation on parallel computers clearly portrayed. Also included are the introductory and fundamental concepts from which the new methods are derived, and on which they are dependent. With the increasing advent of parallel computing into all aspects of computational mathematics, there is no doubt that the new methods will be widely used.
