Numerical Methods of Reactor Analysis
- 1st Edition - January 1, 1964
- Latest edition
- Authors: Melville Clark, Kent F. Hansen
- Editor: V. L. Parsegian
- Language: English
Numerical Methods of Reactor Analysis is an introduction to topics of numerical analysis frequently used in the nuclear reactor field. Emphasis is placed on methods by which… Read more
Purchase options
Data Mining & ML
Unlock the cutting edge
Up to 20% on trusted resources. Build expertise with data mining, ML methods.
Description
Description
Numerical Methods of Reactor Analysis is an introduction to topics of numerical analysis frequently used in the nuclear reactor field. Emphasis is placed on methods by which machine calculations are performed on practical problems related to nuclear reactors. The multigroup diffusion methods and the Monte Carlo method are discussed. Comprised of six chapters, this volume begins by describing a simplified formulation of linear algebra, with emphasis on matrices and operations with matrices as well as the properties of special matrices. Following the introduction of a geometric interpretation of matrix equations, many matrix relations are derived, including relations used in nuclear engineering. The next chapter reviews the elementary properties of finite difference equations, with particular reference to techniques suited to digital computers. Subsequent chapters focus on numerical solutions of equations; multigroup diffusion methods; transport methods; and the Monte Carlo method. This book will be a valuable resource for first and second year graduate students taking an introductory course in reactor physics.
Table of contents
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 B 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
Product details
Product details
- Edition: 1
- Latest edition
- Published: January 28, 1964
- Language: English