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Formulation And Analysis Of Higher Order Finite Difference Approximations To The Neutron Diffusion Equation
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Book Synopsis Formulation and Analysis of Higher Order Finite Difference Approximations to the Neutron Diffusion Equation by : Mohammed Benghanem
Download or read book Formulation and Analysis of Higher Order Finite Difference Approximations to the Neutron Diffusion Equation written by Mohammed Benghanem and published by . This book was released on 1986 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Difference Approximations to the Neutron Diffusion Equation by : H. P. Flatt
Download or read book Finite Difference Approximations to the Neutron Diffusion Equation written by H. P. Flatt and published by . This book was released on 1960 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite difference approximations used in several one-dimensional neutron diffusion codes are studied from the point of view of conservation of neutrons. A new set of approximation formulae is proposed which conserve neutrons. These formulae differ only slightly from earlier formulae, thus allowing a small effect to be corrected by a small amount of effort."
Book Synopsis Lie Group Invariant Finite-difference Schemes for the Neutron Diffusion Equation by : Peter James Jaegers
Download or read book Lie Group Invariant Finite-difference Schemes for the Neutron Diffusion Equation written by Peter James Jaegers and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite difference techniques are used to solve a variety of differential equations. For the neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the mesh spacing squared. To improve the accuracy of the finite difference approximation of the diffusion equation, the invariance properties of the original differential equation have been incorporated into the finite difference equations. Using the concept of an invariant difference operator, the invariant difference approximations of the multi-group neutron diffusion equation were determined in one-dimensional slab and two-dimensional Cartesian coordinates, for multiple region problems. These invariant difference equations were defined to lie upon a cell edged mesh as opposed to the standard difference equations, which lie upon a cell centered mesh. Results for a variety of source approximations showed that the invariant difference equations were able to determine the eigenvalue with greater accuracy, for a given mesh spacing, than the standard difference approximation. The local truncation errors for these invariant difference schemes were found to be highly dependent upon the source approximation used, and the type of source distribution played a greater role in determining the accuracy of the invariant difference scheme than the local truncation error.
Book Synopsis Lie Group Invariant Finite Difference Schemes for the Neutron Diffusion Equation by :
Download or read book Lie Group Invariant Finite Difference Schemes for the Neutron Diffusion Equation written by and published by . This book was released on 1994 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite difference techniques are used to solve a variety of differential equations. For the neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the mesh spacing squared. To improve the accuracy of the finite difference approximation of the diffusion equation, the invariance properties of the original differential equation have been incorporated into the finite difference equations. Using the concept of an invariant difference operator, the invariant difference approximations of the multi-group neutron diffusion equation were determined in one-dimensional slab and two-dimensional Cartesian coordinates, for multiple region problems. These invariant difference equations were defined to lie upon a cell edged mesh as opposed to the standard difference equations, which lie upon a cell centered mesh. Results for a variety of source approximations showed that the invariant difference equations were able to determine the eigenvalue with greater accuracy, for a given mesh spacing, than the standard difference approximation. The local truncation errors for these invariant difference schemes were found to be highly dependent upon the source approximation used, and the type of source distribution played a greater role in determining the accuracy of the invariant difference scheme than the local truncation error.
Book Synopsis Neutron Diffusion by : S. Chakraverty
Download or read book Neutron Diffusion written by S. Chakraverty and published by CRC Press. This book was released on 2017-04-21 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for a systematic understanding of nuclear diffusion theory along with fuzzy/interval/stochastic uncertainty. This will serve to be a benchmark book for graduate & postgraduate students, teachers, engineers and researchers throughout the globe. In view of the recent developments in nuclear engineering, it is important to study the basic concepts of this field along with the diffusion processes for nuclear reactor design. Also, it is known that uncertainty is a must in every field of engineering and science and, in particular, with regards to nuclear-related problems. As such, one may need to understand the nuclear diffusion principles/theories corresponding with reliable and efficient techniques for the solution of such uncertain problems. Accordingly this book aims to provide a new direction for readers with basic concepts of reactor physics as well as neutron diffusion theory. On the other hand, it also includes uncertainty (in terms of fuzzy, interval, stochastic) and their applications in nuclear diffusion problems in a systematic manner, along with recent developments. The underlying concepts of the presented methods in this book may very well be used/extended to various other engineering disciplines viz. electronics, marine, chemical, mining engineering and other sciences such as physics, chemistry, biotechnology etc. This book then can be widely applied wherever one wants to model their physical problems in terms of non-probabilistic methods viz. fuzzy/stochastic for the true essence of the real problems.
Book Synopsis Nonlinear Methods for Solving the Diffusion Equation by : Robert Anthony Shober
Download or read book Nonlinear Methods for Solving the Diffusion Equation written by Robert Anthony Shober and published by . This book was released on 1976 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with methods for the transient solution of the neutron diffusion equations in one or two energy groups. Initially, nonlinear methods for solving the static diffusion equations using the finite element method were investigated. By formulating a new eigenvalue equation, some improvement in the solution efficiency was obtained. However, the transient solution of the diffusion equation using the finite element method was considered to be overly expensive. An analytic method for solving the one-dimensional diffusion equation was then developed. Numerical examples confirmed that this method is exact in one dimension. The method was extended to two dimensions, and results compared employing two different approximations for the transverse leakage. The method based on a flat approximation to the leakage was found to be superior, and it was extended to time-dependent problems. Results of time-dependent test problems show the procedure to be accurate and efficient. Comparisons with conventional finite difference techniques (such as TWIGL or MEKIN) indicate that the scheme can be an order of magnitude more cost effective.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Accuracy Study of Finite Difference Methods by : Nancy Jane Cyrus
Download or read book Accuracy Study of Finite Difference Methods written by Nancy Jane Cyrus and published by . This book was released on 1968 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Equations and Programs for Solutions of the Neutron Group Diffusion Equations by Synthesis Approximations by : S. Kaplan
Download or read book Equations and Programs for Solutions of the Neutron Group Diffusion Equations by Synthesis Approximations written by S. Kaplan and published by . This book was released on 1963 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Difference Solution of the Time Dependent Neutron Group Diffusion Equations by :
Download or read book Finite Difference Solution of the Time Dependent Neutron Group Diffusion Equations written by and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis two unrelated topics of reactor physics are examined: the prompt jump approximation and alternating direction checkerboard methods. In the prompt jump approximation it is assumed that the prompt and delayed neutrons in a nuclear reactor may be described mathematically as being instantaneously in equilibrium with each other. This approximation is applied to the spatially dependent neutron diffusion theory reactor kinetics model. Alternating direction checkerboard methods are a family of finite difference alternating direction methods which may be used to solve the multigroup, multidimension, time-dependent neutron diffusion equations. The reactor mesh grid is not swept line by line or point by point as in implicit or explicit alternating direction methods; instead, the reactor mesh grid may be thought of as a checkerboard in which all the ''red squares'' and '' black squares'' are treated successively. Two members of this family of methods, the ADC and NSADC methods, are at least as good as other alternating direction methods. It has been found that the accuracy of implicit and explicit alternating direction methods can be greatly improved by the application of an exponential transformation. This transformation is incompatible with checkerboard methods. Therefore, a new formulation of the exponential transformation has been developed which is compatible with checkerboard methods and at least as good as the former transformation for other alternating direction methods. (auth).
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1974 with total page 1036 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Research Abstracts written by and published by . This book was released on 1987 with total page 1284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Development and Implementation of Stochastic Neutron Transport Equations and Development and Analysis of Finite Difference and Galerkin Methods for Approximate Solution to Volterra's Population Equation with Diffusion and Noise by : Wyatt Duncan Sharp
Download or read book Development and Implementation of Stochastic Neutron Transport Equations and Development and Analysis of Finite Difference and Galerkin Methods for Approximate Solution to Volterra's Population Equation with Diffusion and Noise written by Wyatt Duncan Sharp and published by . This book was released on 1999 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dissertation Abstracts International by :
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2005 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Comparison Between the Finite Difference and Nodal Integral Methods for the Neutron Diffusion Equation by : Y.Y. Azmy
Download or read book A Comparison Between the Finite Difference and Nodal Integral Methods for the Neutron Diffusion Equation written by Y.Y. Azmy and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Public Works for Water, Pollution Control, and Power Development and Atomic Energy Commission Appropriations for Fiscal Year 1973 by : United States. Congress. Senate. Committee on Appropriations
Download or read book Public Works for Water, Pollution Control, and Power Development and Atomic Energy Commission Appropriations for Fiscal Year 1973 written by United States. Congress. Senate. Committee on Appropriations and published by . This book was released on 1972 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt:
