Numerical Methods of Reactor Analysis - 1st Edition - ISBN: 9780123956538, 9780323154673

Numerical Methods of Reactor Analysis

1st Edition

Editors: Melville Jr. Clark
eBook ISBN: 9780323154673
Imprint: Academic Press
Published Date: 1st January 1964
Page Count: 352
Tax/VAT will be calculated at check-out Price includes VAT (GST)
30% off
30% off
30% off
30% off
30% off
20% off
20% off
30% off
30% off
30% off
30% off
30% off
20% off
20% off
30% off
30% off
30% off
30% off
30% off
20% off
20% off
54.95
38.47
38.47
38.47
38.47
38.47
43.96
43.96
43.99
30.79
30.79
30.79
30.79
30.79
35.19
35.19
72.95
51.06
51.06
51.06
51.06
51.06
58.36
58.36
Unavailable
Price includes VAT (GST)
× DRM-Free

Easy - Download and start reading immediately. There’s no activation process to access eBooks; all eBooks are fully searchable, and enabled for copying, pasting, and printing.

Flexible - Read on multiple operating systems and devices. Easily read eBooks on smart phones, computers, or any eBook readers, including Kindle.

Open - Buy once, receive and download all available eBook formats, including PDF, EPUB, and Mobi (for Kindle).

Institutional Access

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.

Description

Nuclear Science and Technology, Volume 3: Numerical Methods of Reactor Analysis presents the numerical analysis frequently used in the nuclear reactor field. This book discusses the numerical approximation for the multigroup diffusion method, which results in simple algebraic equations. Organized into six chapters, this volume starts with an overview of the simplified formulation of linear algebra by defining the matrices and operations with matrices. This text then discusses the properties of special matrices and reviews the elementary properties of finite difference equations. Other chapters consider a variety of methods of obtaining numerical solutions to the approximating equations. The final chapter deals with Monte Carlo method, which is a statistical method for solving statistical or deterministic problems. This book is a valuable resource for nuclear engineers. Students at the graduate level who had an introductory course in reactor physics and a basic course in differential equations will also find this book useful.

Table of Contents


Preface

Chapter I Linear Equations and Matrix Algebra

1.1 Linear Equations and Matrix Notation

1.2 Matrix Operations

1.3 Determinants

1.4 Solution of Simultaneous Equations

1.5 Special Matrices and Their Properties

1.6 Vector Interpretation

1.7 Matrix Functions and Similarity Transformations

1.8 Linear Independence of Vectors and Orthogonalization of Vectors

1.9 Eigenvalues and Eigenvectors

1.10 Nonsymmetric Matrices

1.11 Geometric Interpretation

1.12 Biorthogonal Vectors

1.13 Nonnegative Matrices

1.14 Special Forms and Matrix Factorization

References

Problems

Chapter II Difference Equations

2.1 A Simple Example

2.2 Difference and Summation Operators

2.3 Formation of Difference Equations and Truncation Error

2.4 Analytic Solution of Difference Equations

2.5 Partial Difference Equations

2.6 Convergence of Difference Solutions

2.7 Matrix Form of Difference Equations

References

Problems

Chapter III Numerical Solutions of Equations

3.1 Numerical Integration

3.2 Ordinary Differential Equations

3.3 Partial Differential Equations

3.4 Hyperbolic Equations

3.5 Parabolic Equations

3.6 Elliptic Equations and Iterative Methods

References

Problems

Chapter IV Multigroup Diffusion Methods

4.1 Age-Diffusion Approximation

4.2 Adjoint Equations

4.3 Formation of Multigroup Equations

4.4 Adjoint Multigroup Equations

4.5 Multigroup Difference Equations

4.6 Matrix Form of Multigroup Equations

4.7 Numerical Solution of the Multigroup Equations

References

Problems

Chapter V Transport Methods

5.1 The PN Approximation

5.2 Double PN Approximation

5.3 Multigroup Transport Methods

5.4 Discrete Ordinate Methods

5.5 The SN Method

5.6 Time Dependent Transport Methods

5.7 Moments Method

References

Problems

Chapter VI The Monte Carlo Method

6.1 Introduction

6.2 Random Numbers

6.3 Distribution Functions

6.4 Statistical Estimation

6.5 Analogs of Two Simple Problems

6.6 Monte Carlo Calculation of the Fast Fission Factor

6.7 Variance Reduction Methods

6.8 Concluding Remarks

References

Problems

Appendix A The Boltzmann Transport Equation

Text

References

Problems

Appendix Β Velocity Relations for Nuclear Events

B.1 Kinematical Relations

B.2 Conservation of Momentum

B.3 Conservation of Energy

B.4 Relation between the Initial and Final Speeds and the Angle of Scattering

B.5 Relation between the Scattering Angles in the Laboratory and the Center-of-Mass System

B.6 Relations among the Scattering Angles and the Initial and Final Energies

B.7 Relations between the Direction Cosines of the Velocity of a Scattered Neutron in the Laboratory System and in a Center-of-Mass System

B.8 Relations between the Direction Cosines of a Scattered Neutron in Two Center-of-Mass Systems

B.9 Transfer Probabilities for Elastic, Isotropic Scattering and Fission

References

Problems

Appendix C Moments Method for Neutrons

Text

References

Appendix D Special Functions

Text

References

Index

Details

No. of pages:
352
Language:
English
Copyright:
© Academic Press 1964
Published:
Imprint:
Academic Press
eBook ISBN:
9780323154673

About the Editor

Melville Jr. Clark