The Methods and Applications of Discrete Ordinates in Low Energy Neutron-Photon Transport (ANISN, DOT). Part I: Methods

  • W. W. EngleJr.
Part of the Ettore Majorana International Science Series book series (EMISS, volume 3)


Lecture 2 contained a brief introduction to the differential form of the Boltzman transport equation which is solved by the discrete ordinates codes. A rather complete description of the derivation of the finite difference form of the transport equation can be found in Reference 1; therefore that derivation will not be discussed here. Attention will be focused on the additional equations required to solve the transport equation which are often referred to as flux models and on the iteration process and efforts to accelerate the convergence of the iteration process. All equations discussed here will be limited to the one-dimensional, time-independent case, but they may be extended in a straightforward manner to multidimensional, time-dependent geometries.


Step Model Flux Model Dominance Ratio Discrete Ordinate Angular Interval 
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  1. 1.
    F. R. Mynatt, F. J. Muckenthaler, and P. N. Stevens, “Development of Two-Dimensional Discrete Ordinates Transport Theory for Radiation Shielding,” CTC-INF-952 (1969).Google Scholar
  2. 2.
    W. H. Reed, “The Effectiveness of Acceleration Techniques for Iterative Methods in Transport Theory,” Nucl. Sci. Eng., 45:245–254 (1971).Google Scholar
  3. 3.
    W. W. Engle, Jr., “Users Manual for ANISN,” K-1693 (1967).Google Scholar
  4. 4.
    W. A. Rhoades, D. B. Simpson, R. L. Childs, and W. W. Engle, Jr., ”The DOT IV Two-Dimensional Discrete Ordinates Transport Code with Space-Dependent Mesh and Quadrature,” ORNL/TM-6529 (August 1978).Google Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • W. W. EngleJr.
    • 1
  1. 1.Oak Ridge National LaboratoryOak RidgeUSA

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