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

- 12 Want to read
- 32 Currently reading

Published
**1979** by Dept. of Energy, [Office of Energy Technology], Oak Ridge National Laboratory, for sale by the National Technical Information Service in Oak Ridge, Tenn, Springfield, Va .

Written in English

- Neutron transport theory,
- Iterative methods (Mathematics),
- Eigenvalues

**Edition Notes**

Statement | D. R. Vondy, and T. B. Fowler |

Series | ORNL/TM ; 6843 |

Contributions | Fowler, T. B., joint author, Oak Ridge National Laboratory |

The Physical Object | |
---|---|

Pagination | v, 31 p. : |

Number of Pages | 31 |

ID Numbers | |

Open Library | OL14881865M |

Counterexamples are used to motivate the revision of the established theory of tracer transport. Then dynamic contrast enhanced magnetic resonance imaging in particular is conceptualized in terms of a fully distributed convection–diffusion model from which a widely used convolution model is derived using, alternatively, compartmental discretizations or semigroup by: 6. Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory. (source: Nielsen Book Data) This book provides a modern investigation into the bifurcation phenomena of physical and engineering problems.

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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 = { }.

This paper gives a survey over some of the most important methods and results of nonlinear functional analysis in ordered Banach spaces. By means of iterative techniques and by using topological tools, fixed point theorems for completely continuous maps in ordered Banach spaces are deduced, and particular attention is paid to the derivation of multiplicity by: ().

Jacobian-Free Newton-Krylov Nodal Expansion Methods with Physics-Based Preconditioner and Local Elimination for Three-Dimensional and Multigroup k-Eigenvalue Problems.

Nuclear Science and Engineering: Vol.No. 3, pp. Cited by: 2. @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. Case, F. De Hoffmann, G. Placzek] on *FREE* shipping on qualifying offers. Introduction to the Theory of Neutron Diffusion [Volume 1]Author: K.

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. Introduction to the theory of neutron diffusion, v.1 [Case, K. M] on *FREE* shipping on qualifying offers. Introduction to the theory of neutron diffusion, v.1Author: K.

M Case. behavior. – Monte Carlo calculates “tallies” for quantities (e.g., reaction rates) that are mean values of the underlying radiation physics. – Because the tally quantities correspond to those from the neutron transport equation, its solution can be inferred.

• The eigenvalue problem is solved iteratively –File Size: 1MB. Neutron transport is the study of the motions and interactions of neutrons with materials.

Nuclear scientists and engineers often need to know where neutrons are in an apparatus, what direction they are going, and how quickly they are moving. It is commonly used to determine the behavior of nuclear reactor cores and experimental or industrial neutron beams.

The neutronics solution without any coupled feedback is essentially a linear generalized eigenvalue problem that computes the fundamental eigenvalue, eigenmode pair. The neutronics solver assumes constant material-dependent temperature/density values to initiate computation of cross sections which are nominal values obtained with the initial Cited by: 3.

Some results on the eigenfunctions. In this section we study the eigenfunctions of the nonlocal problem in the ball B R.

The eigenfunction problem was studied in [] in the L 2 is, in [] the authors consider the family of eigenfunctions normalized as to have the L 2 (B R)-norm equal to 1 and prove that, when properly rescaled, they converge to the unique positive eigenfunction Author: Ariel Salort, Joana Terra, Noemi Wolanski.

Nuclear Technology / Volume / Number 2 / May / Pages to efficiently and accurately evaluate a reactor core’s eigenvalue and power distribution versus burnup using a nodal diffusion generalized perturbation theory (GPT) model is developed.

When compared with a standard nonlinear iterative NEM forward flux solve with. We have studied an inverse problem of recovering the potential in the fractional diffusion model from fixed-time flux data for a set of input sources.

The unique identifiability of the inverse problem has been established in the case where the set of input sources forms a complete basis in L 2 (0, 1) and the time is sufficiently large.

Finite Element Methods for Computational Fluid Dynamics: A Practical Guide - Ebook written by Dmitri Kuzmin, Jari Hamalainen. Read this book using Google Play Books app on your PC, android, iOS devices.

Download for offline reading, highlight, bookmark or take notes while you read Finite Element Methods for Computational Fluid Dynamics: A Practical Guide. The mass flux is specified as (4) where is the diffusion coefficient; this definition has been used to simulate fission product transport within the fuel.

Also implemented in Bison is a hyperstoichiometric model for oxygen diffusion in fuel as described in Newman et al. (). Application to elasticity problems, thermal conduction, and other problems of engineering and physics. Offered: W. View course details in MyPlan: A A A A Finite Element Analysis II (3) Advanced concepts of the finite element method.

Hybrid and boundary element methods. Nonlinear, eigenvalue, and time-dependent problems. In special cases (e.g. 1-D), there can be an analytical solution for two group diffusion theory, basically solving two simultaneous linear differential equations.

However, for most practical (real-world) cases, the two group diffusion theory requires a numerical solution. Most modern nuclear design codes use a modified 2 group approach.General. Validated numerics; Iterative method; Rate of convergence — the speed at which a convergent sequence approaches its limit.

Order of accuracy — rate at which numerical solution of differential equation converges to exact solution; Series acceleration — methods to accelerate the speed of convergence of a series.

Aitken's delta-squared process — most useful for linearly.