Computational methods of neutron transport theory. (English) Zbl 0594.65096

Lewis, E. E.; Miller, W. F. jun.

New York: John Wiley & Sons, Inc. 396 p. $ 44.95 (1985).

[From the Book review in Transport Theory and Statistical Physics 15, 693-695 (1986)]
This book is intended to be used in a first year graduate course for students with little more mathematical background than found in an undergraduate engineering curriculum. For this reason, the first chapter provides the vocabulary of neutron transport theory and the heuristic derivation of the neutron transport equation for readers not familiar with neutron physics. Next, the fundamentals of the discrete ordinate method, one of the most commonly used numerical methods in the nuclear industry, are described. The authors first present the energy discretization scheme and a comprehensive survey of acceleration methods for nuclear reactor criticality calculations. Chapter 4 clearly details the basis for the various quadrature sets, along with the spatial and angular differencing scheme. For completeness, Chapters 5 and 6 present the less popular deterministic methods of collision probability and finite elements associated with the even parity form of the transport equation. In the final chapter, the fundamentals of the Monte Carlo method are briefly reviewed to provide an alternative to deterministic methods.

Reviewer: Barry D.Ganapol

MSC:

65R20	Numerical methods for integral equations
65-02	Research exposition (monographs, survey articles) pertaining to numerical analysis
82C70	Transport processes in time-dependent statistical mechanics
45K05	Integro-partial differential equations
82D45	Statistical mechanical studies of ferroelectrics
65C05	Monte Carlo methods

Keywords:

neutron transport theory; discrete ordinate method; energy discretization scheme; acceleration methods; spatial and angular differencing scheme; methods of collision probability; finite elements; Monte Carlo method