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Saturday, July 18, 2020 | History

2 edition of iterative behavior of diffusion theory flux eigenvalue neutronics problems found in the catalog.

iterative behavior of diffusion theory flux eigenvalue neutronics problems

D. R Vondy

# iterative behavior of diffusion theory flux eigenvalue neutronics problems

## by D. R Vondy

Subjects:
• Neutron transport theory,
• Iterative methods (Mathematics),
• Eigenvalues

• Edition Notes

The Physical Object ID Numbers Statement D. R. Vondy, and T. B. Fowler Series ORNL/TM ; 6843 Contributions Fowler, T. B., joint author, Oak Ridge National Laboratory Pagination v, 31 p. : Number of Pages 31 Open Library OL14881865M

@article{osti_, title = {DIF3D: a code to solve one-, two-, and three-dimensional finite-difference diffusion theory problems. [LMFBR]}, author = {Derstine, K L}, abstractNote = {The mathematical development and numerical solution of the finite-difference equations are summarized. The report provides a guide for user application and details the programming structure of DIF3D. I am trying to calculate the eigenfunctions of the eigenvalue equation using this output from the diffusion equation. The eigenvalue equation is if the form $\textbf{Ax} = \lambda \mathbf{Qx}$. Am I wrong in thinking that the eigenvalues and corresponding eigenvectors of $\textbf{A}$ (from the diffusion equation) will also be valid for the.

Diffusion Theory Anne Johnston February I was first introduced to diffusion theory in the early ’s when I took a communication and social change class as part of my Ph.D. coursework. Following that course, I thought of diffusion of innovations as a theory or model that applied to situations where developed countries attempted to enactFile Size: KB. Introduction to the Theory of Neutron Diffusion [Volume 1] [K. M. Case, F. De Hoffmann, G. Placzek] on *FREE* shipping on qualifying offers. Introduction to the Theory of Neutron Diffusion [Volume 1]Author: K. M. Case, F. De Hoffmann, G. Placzek.

In nuclear engineering, the λ -modes associated with the neutron diffusion equation are applied to study the criticality of reactors and to develop modal methods for the transient analysis. The differential eigenvalue problem that needs to be solved is discretized using a finite element method, obtaining a generalized algebraic eigenvalue problem whose associated matrices are large and : Amanda Carreño, Luca Bergamaschi, Angeles Martinez, Antoni Vidal-Ferrándiz, Damian Ginestar, Gumersi. Expansion Method for Eigenvalue, Adjoint, Fixed-Source Steady-State and Transient ," in "Argonne Code Center: Benchmark Problem Book," Argonne National Laboratory report ANL, Supplement 2 (June ). Solving Multigroup Neutronics Problems Applying the Finite-Difference Diffusion- Theory Approximation to Neutron Transport," Oak Author: R.D. Mosteller.

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### Iterative behavior of diffusion theory flux eigenvalue neutronics problems by D. R Vondy Download PDF EPUB FB2

Get this from a library. The iterative behavior of diffusion theory flux eigenvalue neutronics problems. [D R Vondy; T B Fowler; Oak Ridge National Laboratory.]. chapter reviews the essential details of these two types of problems. The Eigenvalue Problem For a computational node m in Cartesian geometry, the time-dependent behavior of the neu-tron flux is governed by the following nodal balance equations, given in terms of the node-aver-age flux (), precursor density (), the surface average net File Size: KB.

ITERATIVE METHODS FOR EQUIVALENT DIFFUSION THEORY PARAMETERS We start from the multigroup diffusion equations written for the whole core G -V- DgVCg q- E,g = ~-~(hX, U~fh~h q- Eh,) (I) h where h is the eigenvalue, Og is the group-g heterogeneous flux and the cross section notation is Cited by: Chapter 4: The Diffusion Equation Introduction We have seen that the transport equation is exact, but difficult to solve.

Moreover, we only really need the scalar flux ⃗, since we really want to compute reaction rates. In order to obtain that, we must then use the diffusion.

The objective of this paper is to present a foundational theory for the Fourier stability analysis of k-eigenvalue transport problems with flux-dependent cross section feedback. The value of providing such a theory is threefold: (1) it provides a pedagogical example to illuminate the fundamental nature of coupled iteration schemes for reactor Cited by: 2.

It consists of two primary components: (1) a grey (one-group) diffusion eigenvalue problem that is solved via Wielandt-shifted power iteration (PI) and (2) a multigrid-in-space linear solver.

Information is presented about the iterative behavior of selected reactor neutronics problems applying the finite-difference diffusion theory approximation to neutron transport.

The neutron flux distribution in the core is now determined by solving Eqs. (6) and (7) alternately. The neutron flux convergence criterion is given by If the neutron flux distribution satisfies the above condition, the leakage coeffieients also satisfy the following condition, as is readily seen from Eqs.

(4), (5) and (8). The book contains a collection of mathematical solutions of the differential The mathematical theory of diffusion is founded on that of heat conduction These authors present many solutions of the equation of heat conduction and some of them can be applied to diffusion problems for which the diffusion coefficient is constant.

I have. neutronics will commit to perform calculations on three benchmark problems related to neutronics calculations in lattice and core levels. This paper presents the results of the second benchmark problem, i.e. the IAEA 3-D PWR, utilizing the NESTLE core simulator which is based on the diffusion theory with finite difference and nodal method solvers.

The calculation of alpha eigenvalues has traditionally been accomplished using iterative search procedures where an eigenvalue is determined by finding the value of. α that makes the equivalent. k-eigenvalue problem exactly critical.

5 T. HILL, “ Efficient Methods for Time-Absorption Eigenvalue Calculations,” Proc. Advances in Reactor Cited by: 4. The neutron-flux-eigenvalue problems are solved by direct iteration to determine the multiplica- tion factor or the nuclide densities required for a critical system.

CITATIONVP2: Algorithms for the inner-outer iterative calculations are adapted to vector computers. Characteristic (See also Eigenvalue) determinental equation, valu problem, 94 value problem, generalization of 99 Chebyshev modified semi-iterative method, polynomial, semi-iterative method, Chernick, J.

58 70 Chord length, average 63 Coefficient delayed delayed temperature, 6 Doppler temperature 5/4/10 Theory Manual for the PARCS Kinetics Core Simulator Module 6 2. BASIC NEUTRONICS PROBLEMS Two basic types of neutronics problems are solved in PARCS, the eigenvalue problem and the fixed source problem.

The eigenvalue problem is solved during the steady-state initialization prior to a transient, as well as during fuel depletion analysis. The solution of K-eigenvalue problem is commonly required for the analysis of fission -based systems. The prime interest is to evaluate the fundamental mode eigenvalue (K -eff) and the associated shape of neutron flux.

The problem is usually solved by the power iteration method, to find the. This comprehensive volume offers readers a progressive and highly detailed introduction to the complex behavior of neutrons in general, and in the context of nuclear power generation.

A compendium and handbook for nuclear engineers, a source of teaching material for academic lecturers as well as a graduate text for advanced students and other non-experts wishing to enter this field, it is. n this paper we propose a new method for the iterative computation of a few of the extremal.

eigenvalues of a symmetric matrix and their associated eigenvectors. The method is Cited by: Abstract. Pioneering work on the diffusion of neutrons through heterogeneous media was published by Behrens (1) inand thus, some of the methods that are used today to deal with neutron streaming processes already have been evolving for 30 those 30 years, streaming computational techniques, jointly with a body of underlying theory, have been developed with great by: @article{osti_, title = {National Energy Software Center: benchmark problem book.

Revision}, author = {}, abstractNote = {Computational benchmarks are given for the following problems: (1) Finite-difference, diffusion theory calculation of a highly nonseparable reactor, (2) Iterative solutions for multigroup two-dimensional neutron diffusion HTGR problem, (3) Reference solution to the.

The neutronics problem results. A reactor physicist has to play a clever game of takes many forms and some space is devoted to outlining how compromise between expediency and accuracy.

Thus, instead such problems arise, e.g. multigroup eigenvalue, nonlinear. Jean-Pierre Aubin, Approximation of elliptic boundary-value problems, Wiley-Interscience, New-York, USA ISBN, be difficult as a first approach to physicists owing to its very mathematical language.

Nevertheless, several theorems for neutron diffusion theory and the errors due to the approximation of linear operators may be : Serge Marguet.The neutron diffusion equation is often used to perform core-level neutronic calculations.

It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term using a structured grid.

This work introduces the alternatives that unstructured grids can provide Cited by: 6.title = {{Krylov Iterative Methods and the Degraded Effectiveness of Diffusion Synthetic Acceleration for Multidimensional SN Calculations in Problems with Material Discontinuities}}, volume = { }.