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Finite Difference Solution Of The Time Dependent Neutron Group Diffusion Equations
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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).
Book Synopsis Finite Difference Solution of the Time Dependent Neutron Group Diffusion Equations by : John Stanley Hendricks
Download or read book Finite Difference Solution of the Time Dependent Neutron Group Diffusion Equations written by John Stanley Hendricks and published by . This book was released on 1975 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis STREAK, a Numerical Solution for Space-time Neutron Diffusion Equations by : James W. Smiley
Download or read book STREAK, a Numerical Solution for Space-time Neutron Diffusion Equations written by James W. Smiley and published by . This book was released on 1966 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Space-time Flux Synthesis Methods for the Approximate Solution of Time-dependent Boltzmann Neutron Transport Equation by : V. Luco
Download or read book Space-time Flux Synthesis Methods for the Approximate Solution of Time-dependent Boltzmann Neutron Transport Equation written by V. Luco and published by . This book was released on 1966 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Eigenvalue Methods for Time-dependent Neutron Diffusion by : Roberto Gomes de Oliveira
Download or read book Eigenvalue Methods for Time-dependent Neutron Diffusion written by Roberto Gomes de Oliveira and published by . This book was released on 1969 with total page 214 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 Numerical Formulation and Solution of Neutron Transport Problems by : Bengt G. Carlson
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:
Book Synopsis On the Relaxation of the Numerical Stability Criterion in Finite-difference Solutions of the Time-dependent Neutron Diffusion Equations by : James William Smiley
Download or read book On the Relaxation of the Numerical Stability Criterion in Finite-difference Solutions of the Time-dependent Neutron Diffusion Equations written by James William Smiley and published by . This book was released on with total page 162 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 Numerical Methods and Techniques Used in the Two-dimensional Neutron-diffusion Program PDQ-5 by : L. A. Hageman
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:
Book Synopsis The Twenty Grand Program for the Numerical Solution of Few-group Neutron Diffusion Equations in Two Dimensions by : M. L. Tobias
Download or read book The Twenty Grand Program for the Numerical Solution of Few-group Neutron Diffusion Equations in Two Dimensions written by M. L. Tobias and published by . This book was released on 1962 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of Transient and Steady-state Neutron Transport Problems by : Bengt G. Carlson
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:
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.
Book Synopsis Numerical Solution of the Space and Time-dependent Neutron Diffusion Equations by : William Rutledge Rhyne
Download or read book Numerical Solution of the Space and Time-dependent Neutron Diffusion Equations written by William Rutledge Rhyne and published by . This book was released on 1969 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NESTLE written by and published by . This book was released on 1994 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation.
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.
