Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
A class of acceleration schemes is investigated which resembles the conventional synthetic method in that they utilize the diffusion operator in the transport iteration schemes. The accelerated iteration involves alternate diffusion and transport solutions where coupling between the equations is achieved by using a correction term applied to either the diffusion coefficient, the removal cross section, or the source of the diffusion equation. The methods involving the modification of the diffusion coefficient and of the removal term yield nonlinear acceleration schemes and are used in k/sub eff/ calculations, while the source term modification approach is linear at least before discretization, and is used for inhomogeneous source problems. A careful analysis shows that there is a preferred differencing method which eliminates the previously observed instability of the conventional synthetic method. Use of this preferred difference scheme results in an acceleration method which is at the same time stable and efficient. This preferred difference approach renders the source correction scheme, which is linear in its continuous form, nonlinear in its differenced form. An additional feature of these approaches is that they may be used as schemes for obtaining improved diffusion solutions for approximately twice the cost of a diffusion calculation. Numerical experimentation on a wide range of problems in one and two dimensions indicates that improvement from a factor of two to ten over rebalance or Chebyshev acceleration is obtained. The improvement is most pronounced in problems with large regions of scattering material where the unaccelerated transport solutions converge very slowly.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
The diffusion-synthetic acceleration (DSA) method is an iterative procedure for obtaining numerical solutions of discrete-ordinates problems. The DSA method is operationally more complicated than the standard source-iteration (SI) method, but if encoded properly it converges much more rapidly, especially for problems with diffusion-like regions. In this article we describe the basic ideas beind the DSA method and give a (roughly chronological) review of its long development. We conclude with a discussion which covers additional topics, including some remaining open problems and the status of current efforts aimed at solving these problems.
Author: Greenberg Publisher: Birkhäuser ISBN: 303485675X Category : Science Languages : en Pages : 339
Book Description
The Eleventh International Transport Theory Conference and Symposium in honor of the sixty-fifth birthday of Kenneth Case and the sixtieth birthday of Paul Zweifel was held in Blacksburg, Virginia, during May 22-26, 1989, on the campus of Virginia Polytechnic Institute and State University (Virginia Tech). This volume consists of a selection of the invited papers delivered at the Conference, and represents a cross section of the research currently being carried out in the field of transport theory. The volume is divided into two sections. The Symposium lectures are intended each to summarize an important aspect of transport theory, as well as to present timely new results of the author's research interest. The Conference lectures are contributions of each author on his current research. As has been the custom in this series of conferences, each lecturer was invited to participate by the organizing committee of the Conference: W. Greenberg, Virginia Tech, chairman; V. Boffi, Universita di Firenze; N. Corngold, California Institute of Technology; B. Ganapol, University of Arizona; N. McCormick, University of Washington; P. Nelson, Texas Tech; G. Pomraning, University of California, Los Angeles. The Eleventh International Transport Theory Conference was funded by generous con tributions from Science Applications International Corporation, R. Beyster, president, and from Virginia Polytechnic Institute and State University. Conference participants, and, we believe, researchers in this and related areas, are indebted to these organizations. We would like to thank Lamberto Rondoni, in the graduate program at Virginia Tech, for proofreading manuscripts of all the Italian contributors.
Author: Jeremiah U. Brackbill Publisher: Academic Press ISBN: 1483257568 Category : Mathematics Languages : en Pages : 457
Book Description
Multiple Time Scales presents various numerical methods for solving multiple-time-scale problems. The selection first elaborates on considerations on solving problems with multiple scales; problems with different time scales; and nonlinear normal-mode initialization of numerical weather prediction models. Discussions focus on analysis of observations, nonlinear analysis, systems of ordinary differential equations, and numerical methods for problems with multiple scales. The text then examines the diffusion-synthetic acceleration of transport iterations, with application to a radiation hydrodynamics problem and implicit methods in combustion and chemical kinetics modeling. The publication ponders on molecular dynamics and Monte Carlo simulations of rare events; direct implicit plasma simulation; orbit averaging and subcycling in particle simulation of plasmas; and hybrid and collisional implicit plasma simulation models. Topics include basic moment method, electron subcycling, gyroaveraged particle simulation, and the electromagnetic direct implicit method. The selection is a valuable reference for researchers interested in pursuing further research on the use of numerical methods in solving multiple-time-scale problems.
Author: Yousry Azmy Publisher: Springer Science & Business Media ISBN: 9048134110 Category : Technology & Engineering Languages : en Pages : 476
Book Description
Nuclear engineering has undergone extensive progress over the years. In the past century, colossal developments have been made and with specific reference to the mathematical theory and computational science underlying this discipline, advances in areas such as high-order discretization methods, Krylov Methods and Iteration Acceleration have steadily grown. Nuclear Computational Science: A Century in Review addresses these topics and many more; topics which hold special ties to the first half of the century, and topics focused around the unique combination of nuclear engineering, computational science and mathematical theory. Comprising eight chapters, Nuclear Computational Science: A Century in Review incorporates a number of carefully selected issues representing a variety of problems, providing the reader with a wealth of information in both a clear and concise manner. The comprehensive nature of the coverage and the stature of the contributing authors combine to make this a unique landmark publication. Targeting the medium to advanced level academic, this book will appeal to researchers and students with an interest in the progression of mathematical theory and its application to nuclear computational science.
Author: Jeffery Lewins Publisher: Springer Science & Business Media ISBN: 9780306436147 Category : Science Languages : en Pages : 322
Book Description
This twenty-fifth volume in a distinguished series addresses a range of topics including: the difficult matter of questioning scientific hypotheses in court the use of Monte Carlo simulation to evaluate time-dependent development and to study system reliability in nuclear reactors of considerable complexity the genetic optimization algorith wavelet analysis ergonomic design of safer and more efficient plant control rooms.
Author: Frank Graziani Publisher: Springer Science & Business Media ISBN: 3540281258 Category : Computers Languages : en Pages : 539
Book Description
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.
Author: MUSA YAVUZ Publisher: ISBN: Category : Languages : en Pages : 530
Book Description
performance of the new multigrid method degrades with an increasing number of processors, not because of the degradation in the convergence rate, but because of the domination of communication overhead and unemployment of some processors on the coarse grids.
Author: Dan Gabriel Cacuci Publisher: Springer Science & Business Media ISBN: 0387981306 Category : Science Languages : en Pages : 3701
Book Description
This is an authoritative compilation of information regarding methods and data used in all phases of nuclear engineering. Addressing nuclear engineers and scientists at all levels, this book provides a condensed reference on nuclear engineering since 1958.
Author: 
Author: 
Author: Greenberg
Author: Jeremiah U. Brackbill
Author: Yousry Azmy
Author: Jeffery Lewins
Author: Frank Graziani
Author: Alain Hébert
Author: MUSA YAVUZ
Author: Dan Gabriel Cacuci