RSICC Home Page GANAPOL-ABNTT

RSICC CODE PACKAGE MIS-011

1.†††††††† NAME AND TITLE

GANAPOL-ABNTT:†††††† Analytical Benchmarks for Nuclear Engineering Applications: Case Studies in Neutron Transport Theory

2.†††††††† CONTRIBUTORS

University of Arizona, Tucson, AZ, USA, through the OECD Nuclear Energy Agency Data Bank, Issy-les-Moulineaux, France.

3.†††††††† CODING LANGUAGE AND COMPUTER

Fortran 77, PDF format; many computers (M00011MNYCP00).

4.†††††††† NATURE OF PROBLEM SOLVED

The developers of computer codes involving neutron transport theory for nuclear engineering applications seldom apply analytical benchmarking strategies to ensure the quality of their programs. A major reason for this is the lack of analytical benchmarks and documentation in the literature. The few such benchmarks that do exist are difficult to locate, as they are scattered throughout the neutron transport and radiative transfer literature. The motivation for this benchmark compendium is to gather several analytical benchmarks appropriate for nuclear engineering applications under one cover. The following three subject areas are considered: neutron slowing down and thermalization without spatial dependence, one-dimensional neutron transport in infinite and finite media, and multidimensional neutron transport in a half-space and an infinite medium. Each benchmark is briefly described, followed by a detailed derivation of the analytical solution representation. Finally, a demonstration of the evaluation of the solution representation includes qualified numerical benchmark results. All accompanying computer codes are suitable for the PC computational environment and can serve as educational tools for nuclear engineering courses. While this benchmark compilation does not contain all possible benchmarks, it does include some of the most prominent ones and should serve as a valuable reference.

Chapter 1 contains a detailed introduction to the different forms of the transport equation that are solved. Chapter 2 covers slowing down and thermalization in an infinite medium, Chapter 3 deals with one-group space dependent problems, including the classical Greenís function and albedo problems in plane and cylindrical geometries, Chapter 4 presents two multigroup space-dependent applications. The compendium concludes with two multigroup, multidimensional cases in Chapter 5.

Twelve reference calculations in transport theory are presented in order of progressive complexity, from problems in only the energy or only the spatial variables to problems with both variables.

The set of Fortran programs for the benchmarks are included upon request from the OECD/NEA Data Bank. Minor improvements have been implemented in version NEA-1827/02.

The book and the computer codes provide a basis for understanding the fundamental concepts of neutron transport theory. It includes recent theoretical as well as numerical advances in analytical benchmarking. Readers of the book and users of the computer codes provided will become familiar with analytical forms of the transport equation, analytical methods of solutions in various geometries, numerical evaluations of analytical representations, semi-analytical benchmarking techniques.

5.†††††††† METHOD OF SOLUTION

Analytical, semi-analytical solutions, Laplace transform and Fourier transform, Fn method, BL approximation, Gauss quadrature.

6.†††††††† RESTRICTIONS OR LIMITATIONS

Analytical solution representation limits our considerations to relatively simple transport problems. Thus, analytical benchmarks provide limited verification of isolated portions of comprehensive algorithms. Even with limited verification of the components of an algorithm, our goal is to achieve some degree of confidence in the entire operation of a code. Inconsistencies and inaccuracies may remain, however, from interfacing of components and unexercised portions of an algorithm. The author provides training courses using this and additional course material. Recipients are not allowed to start their own training courses using this material without having received explicit authorization from the author.

7.†††††††† TYPICAL RUNNING TIME

Running times may vary but typically less than a minute

8.†††††††† COMPUTER HARDWARE REQUIREMENTS

PC compatible computer.

9.†††††††† COMPUTER SOFTWARE REQUIREMENTS

MS or a UNIX operating systems with a working Fortran-77 compiler. Adobe Acrobat Reader can be used to access the files in Portable Data Format (.pdf).

10.††††††† REFERENCES

B. D. Ganapol, Analytical Benchmarks for Nuclear Engineering Applications, Case Studies in Neutron Transport Theory, NEA/DB(2008)1, ISBN 978-92-64-99056-2, OECD 2008, NEA No. 6292.

11.††††††† CONTENTS OF CODE PACKAGE

The package is transmitted in a WinZIP file which contains the book, source code, Windows executables documentation.

12.††††††† DATE OF ABSTRACT

December 2010.

KEYWORDS:†††††† BENCHMARK NEUTRON FIELDS, NEUTRON, MULTIGROUP