John Wiley & Sons, New York, 1984, 414 pp.
The object of this book is to present a balanced overview of the computational methods currently available for the solution of neutron transport problems encountered in engineering analysis. With changes only in the interaction laws contained in the cross section data, much of the text is equally applicable to other neutral particles, most particularly gamma rays. Moreover, several of the numerical methods developed for the linear equations of neutral particle transport are finding increased use in conjunction with nonlinear transport problems, such as those encountered in gas dynamics, plasma physics, and electron transport.
An attempt has been made to make the book reasonably self-contained in the hope that it may serve both as a text for first-year graduate students and as a reference to the practicing engineer. The subject matter relates strongly to the physics of nuclear reactors and radiation shielding on the one hand and numerical analysis on the other. Previous exposure to an introductory course in reactor theory is very helpful. For while we attempt to include all the necessary physical concepts, the choice of an effective computational method most often rests strongly on a thorough understanding of the underlying physics of the problem. A mathematics background through linear algebra and differential equations is presumed.Contents
The Transport Equation.
Introduction.
Particle Interactions.
Particle Streaming.
Transport with Secondary Particles.
The Time-Independent Transport Equation.
The Adjoint Transport Equation.
References.
Problems.
Energy and Time Discretization.
Introduction.
The Multigroup Equations.
Fixed Source Problems.
Criticality Calculations.
Time-Dependent Problems.
References.
Problems.
Discrete Ordinates Methods In One Spatial Dimension.
Introduction.
Angular Approximations.
Spatial Differencing and Solution.
Curvilinear Coordinates.
Acceleration.
References.
Problems.
Multidimensional Discrete Ordinates Methods.
Introduction.
Discrete Ordinates Quadrature Sets.
Difference Equations: Cartesian Coordinates.
Difference Equations: Curvilinear Coordinates.
Triangular Mesh Difference Equations.
Ray Effects.
References.
Problems.
Integral Transport Methods.
Introduction.
Derivation of the Integral Equations.
Slab Geometry.
Integral Transport in Two Dimensions.
Application of Integral Transport Methods.
Evaluation of Collision Probabilities.
References.
Problems.
Even-Parity Transport Methods.
Introduction.
The Even-Parity Transport Formulation.
Spatial Finite Elements.
Slab Geometry Transport Methods.
Two-Dimensional Transport.
References.
Problems.
The Monte Carlo Method.
Introduction.
Probability Distribution Functions.
Analog Monte Carlo Sampling.
Error Estimates.
An Example Calculation.
Nonanalog Monte Carlo.
Tracking in Phase Space.
Criticality Calculations.
References.
Problems.Appendixes.
Index.
