CCC-0276: GRUNCLE, 1st Collision Source Calculation for Program DOT<br>DOT-3.5, 2-D Neutron Transport, Gamma Transport Program DOT with New Space-Scaling

Program-name Package-ID Status DGRAD/TPERT CCC-0276/01 Tested DOT-3.5 CCC-0276/02 Tested GRTUNCL CCC-0276/03 Tested VIP CCC-0276/04 Tested DOT-3.5 CCC-0276/05 Obsolete DOT-3.5 CCC-0276/06 Obsolete DOT-3.5/E CCC-0276/07 Tested DOT-3.5/E CCC-0276/08 Obsolete DUCT CCC-0276/09 Tested DOT-3 CCC-0276/10 Obsolete DOT-3 CCC-0276/11 Obsolete DOT-3 CCC-0276/12 Obsolete DOT-3 CCC-0276/13 Obsolete DOT-3 CCC-0276/14 Obsolete DUCT CCC-0276/15 Obsolete DOT-3.5/E CCC-0276/16 Obsolete DOT-3.5/CAB CCC-0276/17 Obsolete DOT-3.5 CCC-0276/18 Obsolete DOT-3.5/CAB CCC-0276/19 Obsolete

Machines used: Package-ID Orig.Computer Test Computer CCC-0276/01 IBM 360 series IBM 370 series CCC-0276/02 IBM 370 series IBM 370 series CCC-0276/03 IBM 370 series IBM 370 series CCC-0276/04 IBM 370 series IBM 370 series CCC-0276/07 IBM 370 series IBM 370 series CCC-0276/09 IBM 370 series IBM 370 series

3. NATURE OF PROBLEM OR FUNCTION - DOT solves the Boltzmann transport equation in two-dimensional geometries. Principal applications are to neutron and/or photon transport, although the code can be applied to transport problems for any particles not subject to external force fields. Both homogeneous andexternal-source problems can be solved. Searches on multiplication factor, time absorption, nuclide concentration, and zone thickness are available for reactor problems. Numerous edits and output data sets for subsequent use are available.
DOT-3.5 improves the space-scaling algorithm.
DOT-3.5/CAB contains group by group UPSCATTER scaling method.
DUCT calculates perturbations to the scalar flux caused by the presence of ducts filled with coolant.
VIP is a program for cross section sensitivity analysis using two- dimensional discrete ordinates transport calculations.
DGRAD calculates the directional flux gradients from DOT-3 diffusion theory flux tapes. In conjunction with VIP and TPERT, it allows the use of diffusion theory fluxes to obtain exact and first-order perturbation reactivity changes. In order to calculate the reactivity associated with changes in reactor compositions using diffusion theory, it is necessary to fold not only the scalar fluxes with the appropriate cross sections, but also the average flux gradients with the diffusion coefficients. Since DOT diffusion theory does not directly calculate these gradients, it was necessary to calculate the needed quantities external to the DOT code.
TPERT is a perturbation code to obtain exact and first-order reactivity changes. TPERT is coupled to VIP which generates adjoint forward fux tables using DOT-3 scalar flux tape information.
GRTUNCL calculates an analytical first-collision source for subsequent use in DOT.

4. METHOD OF SOLUTION - The method of discrete ordinates is used.
Balance equations are solved for the density of particles moving along discrete directions in each cell of a two-dimensional spatial mesh. Anisotropic scattering is treated using a Legendre expansion of arbitrary order. Convergence can be accelerated by several optional schemes, including a pointwise rescaling technique.
DOT-3.5/E: Differs from DOT-3.5 in that exponential supplementary equations, as well as the usual diamond and weighted schemes, may be used to find the mesh-centre flux from the fluxes at the faces of the mesh.
The model:
1. always gives positive solutions and does not require any fixup techniques provided that the source is non-negative;
2. improves convergence rate in most neutron deep-penetration problems and, for any practical spatial discretization, always requires CPU times not only smaller than those required by DOT-3 mixed (linear + step fixup) model, but also shorter (generally 10-20%) than the times required by DOT-3.5 weighted difference model;
3. increasing spatial mesh size supplies solutions which are always reasonable overestimates of the exact solution and its numerical behaviour is more stable and coherent than the mixed mode.
Experience up to now from several deep penetration problems in (r,z) and (x,y) geometry shows that, while for neutrons the exponential model almost always works very well, for gamma rays its behaviour may be critical and in some cases there is lack of convergence.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM - The total storage requirement is determined by a formula given in the input description. No other restrictions to problem size are applicable.

6. TYPICAL RUNNING TIME - Problems of practical value may range from 0.05 minutes to many hours in running time. A formula given in the input description allows estimation of central processor time for a particular problem.
DOT-3.5/E: In the most deep penetration problems, DOT-3.5/E with exponential model is about 10 to 20 % faster than DOT-3.5 with weighted difference model.

7. UNUSUAL FEATURES OF THE PROGRAM - Flexible dimensioning is used throughout so that only the total storage requirement for a given problem is of concern. The program has two levels of external storage utilization in order to adapt to various problem requirements efficiently. Cross sections can be input on cards, from an ANISN-type nuclide-organized data set, or from a special group-organized data set which is valuable for very large cross section sets. A free-field data input format facilitates problem preparation. Special features which make DOT-3 well adapted to shielding problems include albedo boundary conditions, the capability to output fluxes at exterior or interior boundaries for use in 'bootstrap' problems, and an analytic first-collision source calculation that mitigates ray-streaming effects in certain problems. Upscattering is allowed, and special routines are able to synthesize two-dimensional flux guesses from one-dimensional data produced by the ANISN code. Diffusion theory is also available. The convergence test can be restricted to specified zones.
DOT-3.5/E: Exponential equations to compute mesh centre fluxes.

9. STATUS
CCC-0276/01: 01-SEP-1980 Tested at NEADB
CCC-0276/02: 01-MAY-1979 Tested at NEADB
CCC-0276/03: 01-DEC-1976 Tested at NEADB
CCC-0276/04: 01-MAR-1978 Tested at NEADB
CCC-0276/05: 01-DEC-1976 Obsolete
CCC-0276/06: 24-OCT-1996 Obsolete
CCC-0276/07: 01-MAY-1979 Tested at NEADB
CCC-0276/08: 24-OCT-1996 Obsolete
CCC-0276/09: 01-DEC-1976 Tested at NEADB
CCC-0276/10: 24-OCT-1996 Obsolete
CCC-0276/11: 01-AUG-1975 Obsolete
CCC-0276/12: 01-NOV-1973 Obsolete
CCC-0276/13: 08-APR-1982 Obsolete
CCC-0276/14: 08-APR-1982 Obsolete
CCC-0276/15: 01-NOV-1973 Obsolete
CCC-0276/16: 22-DEC-1995 Obsolete
CCC-0276/17: 24-OCT-1996 Obsolete
CCC-0276/18: 25-MAY-2001 Obsolete
CCC-0276/19: 24-OCT-1996 Obsolete

10. REFERENCES  -
- W. W. Engle, Jr.:
  'A User's Manual for ANISN'
  Computing Technology Center, Union Carbide Corporation
  Report K-1693 (March 30, 1967).
- N.M. Greene, and C.W. Craven, Jr.:
  'XSDRN, A Discrete Ordinates Spectral Averaging Code'
  ORNL-TM-2500 (July 1969).
- W.A. Rhoades:
  'The ALC1 Program for Cross-Section Library Management'
  ORNL-TM-4015 (December 1972).
- Unpublished Notes for GIP, GRTUNCLE, SPACETRAN, FALSTF, ISOPLOT, PLOTTER, PERT-2D, FACT, and DOMINO.
- R. Douglas O'Dell and Raymond E. Alcouffe:
Transport Calculations for Nuclear Analyses: Theory and Guidelines for Effective Use of Transport Codes
  LA-10983-MS and UC-32 (September 1987).
CCC-0276/01:
CCC-0276/02:
- W.A. Rhoades:
  Comments on the DOT 3.5 Version of DOT III (November 1975)
- Utility Network of America:
  Program Additions to DOT 3 (July 1975)
- W.A. Rhoades and F.R. Mynatt:
  The DOT-III Two-Dimensional Discrete Ordinates Transport Code
  ORNL-TM-4280 (September 1973)
- P.A. Read, W.E. Selph and R.J. Cerbone:
  DUCT Code Manual
  Gulf-RT-10654
- J.T. West:
  SORREL (November 1975)
- J.P. Jenal:
  Common Symmetric Quadratures and the DOQDP Computer Code (August
  1975)
- R.L. Childs:
  VIP Input Instructions (November 1976)
- R.L. Childs, D.E. Bartine and W.W. Engle, Jr.:
  Perturbation Theory and Sensitivity Analysis for Two-Dimensional
  Shielding Calculations
  ANS Transactions, Vol. 21, pp. 543-544 (June 1975)
- J.P. Jenal et al.:
  The Generation of a Computer Library for Discrete Ordinates Quadreture Sets
  ORNL/TM-6023 (September 1977)
- E.T. Tomlinson and R.A. Lillie:
  User's Guide and Description of the Perturbation Code Modules
  DGRAD and TPERT
  ORNL/CSD/TM-71 (September 1978)
- NEA-CPL:
  Note on DOT3.5 (12 January 1977)
- OECD/NEA:
  Note from the NEA Data Bank (May 1984)
CCC-0276/03:
CCC-0276/04:
CCC-0276/07:
- W.A. Rhoades:
  Comments on the DOT 3.5 Version of DOT III (November 1975)
- Utility Network of America:
  Program Additions to DOT 3 (July 1975)
- W.A. Rhoades and F.R. Mynatt:
  The DOT-III Two-Dimensional Discrete Ordinates Transport Code
  ORNL-TM-4280 (September 1973)
- P.A. Read, W.E. Selph and R.J. Cerbone:
  DUCT Code Manual
  Gulf-RT-10654
- J.T. West:
  SORREL (November 1975)
- J.P. Jenal:
  Common Symmetric Quadratures and the DOQDP Computer Code
  (August 1975)
- R.L. Childs:
  VIP Input Instructions (November 1976)
- R.L. Childs, D.E. Bartine and W.W. Engle, Jr.:
  Perturbation Theory and Sensitivity Analysis for Two-Dimensional
  Shielding Calculations
  ANS Transactions, Vol. 21, pp. 543-544 (June 1975)
- J.P. Jenal et al.:
  The Generation of a Computer Library for Discrete Ordinates Quadrature Sets
  ORNL/TM-6023 (September 1977)
- E.T. Tomlinson and R.A. Lillie:
  User's Guide and Description of the Perturbation Code Modules
  DGRAD and TPERT
  ORNL/CSD/TM-71 (September 1978)
- NEA-CPL:
  Note on DOT3.5 (12 January 1977)
- OECD/NEA:
  Note from the NEA Data Bank (May 1984)
- L. Erradi:
  Corrections Apportees a DOT-3.5/E - Adaptation sur la Machine
  IBM 4361 (4341) VM.
- P. Barbucci and F. Di Pasquantonio:
  Exponential Supplementary Equations for Sn Methods: The Two-
  Dimensional Case
  Reprint of Paper, Proceedings of Fifth International Conference
  on Reactor Shielding, Knoxville, Tennessee (April 18-22, 1977)
- P. Barbucci and F. Di Pasquantonio:
  Implementation of Exponential Supplementary Equations on DOT-III
  and DOT 3.5 Codes
  (Document received November 1977)
CCC-0276/09:

11. MACHINE REQUIREMENTS - Card input, printed and punched output, and the 3 scratch data sets may be located on any external storage device, as may the 9 optional data sets. A small, but useful, problem can be run in as little as 256k bytes of fast memory. A clock, if available, provides timing data.

12. PROGRAMMING LANGUAGE(S) USED -
CCC-0276/01: FORTRAN-IV
CCC-0276/02: FORTRAN+ASSEMBLER
CCC-0276/03: FORTRAN+ASSEMBLER
CCC-0276/04: FORTRAN-IV
CCC-0276/07: FORTRAN-IV
CCC-0276/09: FORTRAN-IV

13. OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM IS EXECUTED - IBM
360 OS version 16 or later.

14. ANY OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS - This is an improved version of DOT-3 and replaces all previous versions of this code.

15. NAME AND ESTABLISHMENT OF AUTHOR - The DOT code has been developed by Neutron Physics Division
Oak Ridge National Laboratory
Oak Ridge, Tennessee, U.S.A

17. CATEGORIES  -

- C.  Static Design Studies
- J.  Gamma Heating and Shield Design

Keywords: ANISOTROPIC SCATTERING, DISCRETE ORDINATE METHOD, LEGENDRE POLYNOMIALS, NEUTRON TRANSPORT THEORY, TWO-DIMENSIONAL