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Finite Difference Approximations To The Neutron Diffusion Equation
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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 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 The Formulation and Analysis of the Nine-point Finite Difference Approximation for the Neutron Diffusion Equation in Cylindrical Geometry by : Hamza Khudhair Al-Dujaili
Download or read book The Formulation and Analysis of the Nine-point Finite Difference Approximation for the Neutron Diffusion Equation in Cylindrical Geometry written by Hamza Khudhair Al-Dujaili and published by . This book was released on 1975 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 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).
Book Synopsis The FOG One-dimensional Neutron Diffusion Equation Codes by : H. P. Flatt
Download or read book The FOG One-dimensional Neutron Diffusion Equation Codes written by H. P. Flatt and published by . This book was released on 1961 with total page 52 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 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 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 Comparison of Nodal and Finite Difference Methods for Solving the Steady State Multigroup Neutron Diffusion Equation by : Jeremy John Whitlock
Download or read book Comparison of Nodal and Finite Difference Methods for Solving the Steady State Multigroup Neutron Diffusion Equation written by Jeremy John Whitlock and published by . This book was released on 1991 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Exact and Approximate Interior Corner Problem in Neutron Diffusion by Integral Transform Methods by :
Download or read book Exact and Approximate Interior Corner Problem in Neutron Diffusion by Integral Transform Methods written by and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical solution of the neutron diffusion equation exhibits singularities in its derivatives at material corners. A mathematical treatment of the nature of these singularities and its impact on coarse network approximation methods in computational work is presented. The mathematical behavior is deduced from Green's functions, based on a generalized theory for two space dimensions, and the resulting systems of integral equations, as well as from the Kontorovich--Lebedev Transform. The effect on numerical calculations is demonstrated for finite difference and finite element methods for a two-region corner problem.
Book Synopsis Extrapolation Techniques Applied to Matrix Methods in Neutron Diffusion Problems by : Robert R. McCready
Download or read book Extrapolation Techniques Applied to Matrix Methods in Neutron Diffusion Problems written by Robert R. McCready and published by . This book was released on 1956 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: This matrix method is applied to the problem of finding criticality and neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron-diffusion equations is treated. Results for this example are indicated.
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:
