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:
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:
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."
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 Development of a Nodal Method for the Solution of the Neutron Diffusion Equation in General Cylindrical Geometry written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The usual strategy for solving the neutron diffusion equation in two or three dimensions by nodal methods is to reduce the multidimensional partial differential equation to a set of ordinary differential equations (ODEs) in the separate spatial coordinates. This reduction is accomplished by "transverse integration" of the equation.1 For example, in three-dimensional Cartesian coordinates, the three-dimensional equation is first integrated over x and y to obtain an ODE in z, then over x and z to obtain an ODE in y, and finally over y and z to obtain an ODE in x. Then the ODEs are solved to obtain onedimensional solutions for the neutron fluxes averaged over the other two dimensions. These solutions are found in regions ("nodes") small enough for the material properties and cross sections in them to be adequately represented by average values. Because the solution in each node is an exact analytical solution, the nodes can be much larger than the mesh elements used in finite-difference solutions. Then the solutions in the different nodes are coupled by applying interface conditions, ultimately fixing the solutions to the external boundary conditions.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1994-02 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Higher order Nodal Integral Methods for Heat Conduction and Incompressible Fluid Flow written by Peter Donald Esser and published by . This book was released on 1991 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976-05 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Reactors physics Design And Safety Proceedings Of The Workshop written by A Gandini and published by World Scientific. This book was released on 1995-10-24 with total page 1126 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures reported in these proceedings were given in the Workshop on Nuclear Reactors — Physics, Design and Safety held at the International Centre for Theoretical Physics in Trieste in 1994 by experts from leading international research institutions and industries. They have been organized in a self-consistent form with the objective of giving basic, up-dated information to scientists and engineers from developing countries in modern methods for the computation and analysis of nuclear reactors, with particular emphasis on reactor physics, design and safety.
Download or read book Super Light Water Reactors and Super Fast Reactors written by Yoshiaki Oka and published by Springer Science & Business Media. This book was released on 2010-06-28 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Super Light Water Reactors and Super Fast Reactors provides an overview of the design and analysis of nuclear power reactors. Readers will gain the understanding of the conceptual design elements and specific analysis methods of supercritical-pressure light water cooled reactors. Nuclear fuel, reactor core, plant control, plant stand-up and stability are among the topics discussed, in addition to safety system and safety analysis parameters. Providing the fundamentals of reactor design criteria and analysis, this volume is a useful reference to engineers, industry professionals, and graduate students involved with nuclear engineering and energy technology.
Download or read book Government Reports Annual Index written by and published by . This book was released on 1991 with total page 1768 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fluid Mechanics and Fluid Power Volume 3 written by Krishna Mohan Singh and published by Springer Nature. This book was released on 2024-01-16 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises select peer-reviewed proceedings of the 9th International and 49th National Conference on Fluid Mechanics and Fluid Power (FMFP 2022). This book brings together scientific ideas and engineering solutions put forth by researchers and practitioners from academia and industry in the important and ubiquitous field of fluid mechanics. The contents of this book focus on fundamental issues and perspective in fluid mechanics, measurement techniques in fluid mechanics, computational fluid and gas dynamics, instability, transition and turbulence, fluid-structure interaction, multiphase flows, microfluidics, bio-inspired fluid mechanics, aerodynamics, turbomachinery, propulsion and power and other miscellaneous topics in the broad domain of fluid mechanics. This book is a useful reference to researchers and professionals working in the broad field of mechanics.
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.
Download or read book BERRU Predictive Modeling written by Dan Gabriel Cacuci and published by Springer. This book was released on 2018-12-29 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the experimental calibration of best-estimate numerical simulation models. The results of measurements and computations are never exact. Therefore, knowing only the nominal values of experimentally measured or computed quantities is insufficient for applications, particularly since the respective experimental and computed nominal values seldom coincide. In the author’s view, the objective of predictive modeling is to extract “best estimate” values for model parameters and predicted results, together with “best estimate” uncertainties for these parameters and results. To achieve this goal, predictive modeling combines imprecisely known experimental and computational data, which calls for reasoning on the basis of incomplete, error-rich, and occasionally discrepant information. The customary methods used for data assimilation combine experimental and computational information by minimizing an a priori, user-chosen, “cost functional” (usually a quadratic functional that represents the weighted errors between measured and computed responses). In contrast to these user-influenced methods, the BERRU (Best Estimate Results with Reduced Uncertainties) Predictive Modeling methodology developed by the author relies on the thermodynamics-based maximum entropy principle to eliminate the need for relying on minimizing user-chosen functionals, thus generalizing the “data adjustment” and/or the “4D-VAR” data assimilation procedures used in the geophysical sciences. The BERRU predictive modeling methodology also provides a “model validation metric” which quantifies the consistency (agreement/disagreement) between measurements and computations. This “model validation metric” (or “consistency indicator”) is constructed from parameter covariance matrices, response covariance matrices (measured and computed), and response sensitivities to model parameters. Traditional methods for computing response sensitivities are hampered by the “curse of dimensionality,” which makes them impractical for applications to large-scale systems that involve many imprecisely known parameters. Reducing the computational effort required for precisely calculating the response sensitivities is paramount, and the comprehensive adjoint sensitivity analysis methodology developed by the author shows great promise in this regard, as shown in this book. After discarding inconsistent data (if any) using the consistency indicator, the BERRU predictive modeling methodology provides best-estimate values for predicted parameters and responses along with best-estimate reduced uncertainties (i.e., smaller predicted standard deviations) for the predicted quantities. Applying the BERRU methodology yields optimal, experimentally validated, “best estimate” predictive modeling tools for designing new technologies and facilities, while also improving on existing ones.
