1. NAME AND TITLE

DOT: Multigroup Two-Dimensional Discrete Ordinates Transport Code with Anisotropic Scattering.

DOT was first available in 1966. DOT-II was widely distributed, resulting in a proliferation of versions. To simplify maintenance and continue to follow current usage and modifications to DOT, RSIC began to assign new numbers to incoming versions, as follows: CCC-151/DOT 2DB (GE Sunnyvale); CCC-209/DOT III (ORNL); CCC-252/DOT (LSU); CCC-276/DOT 3.5 (ORNL); CCC-319/Dot 3.5/ E (CRTN, Italy); and CCC-320/DOT IV (4.2, ORNL).

The CCC-89/DOT code package contains selected material from early versions retained by RSIC as background information to the DOT series (19661973) and full documentation. It is not recommended for general usage. The computer materials are as follows:

DOT I Source (1968) IBM 7090

DOT II Source (1970) IBM 360/370

DATA Sn Constants (1970)

DO Source (1970) IBM 360/370

DASH Source (1970) IBM 360/370

DOT II-W Source (1973) IBM 360/370

DOT II-W Source (1973) CDC 6600

FIDO Source for Dot-IIW IBM 360/370

2. CONTRIBUTORS

Computer Sciences and Engineering Physics Divisions, Oak Ridge National Laboratory, Oak Ridge, Tennessee.

Atomics International, Canoga Park, California.

Gulf General Atomic, San Diego, California.

U. S. Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico.

Westinghouse Astronuclear Corporation, Pittsburgh, Pennsylvania.

Aerojet Nuclear Systems Company, Sacramento, California.

3. CODING LANGUAGE AND COMPUTER

FORTRAN IV; IBM 7090, IBM 360/75, AND CDC 6600.

4. NATURE OF PROBLEM SOLVED

DOT is a general purpose program which solves the linear, energy-dependent, Boltzmann transport equation for two-dimensional r-z, x-y, and r-theta geometries. The basic form of the solution is the quantity phi bar (ri, zj, Eg, omega d) deltaEg = phiijgd, the flux, averaged in the spatial interval surrounding ri, zj, integrated over the energy group g, and averaged in the solid segment surrounding omegad.

5. METHOD OF SOLUTION

The gradient or convection term in the Boltzmann equation is approximated by a finite difference technique known as discrete ordinates Carlson's Sn method. The inscatter integral is approximated by expanding the differential cross-section in a Legendre series which allows the integral to be computed by quadrature. DOT will solve forward or adjoint, homogeneous or inhomogeneous problems. The inhomogeneous problems may have a volume distributed source or a specified angular flux at the right or top boundaries; fissions may be included for a subcritical system. Homogeneous (eigenvalue) problems will determine the following: (1) static multiplication factor, ``k,'' (2) time absorption, ``Rossia,'' (3) concentration for a specified k, (4) zone thickness for a specified k.

The primary differences between DDK and DOT are given in the following: general anisotropic scattering is allowed, boundary sources may be treated by specifying the angular flux at the right or top boundaries, angular fluxes may be printed or written on binary tape, the pass B scaling for problems with reflected right or top boundaries has been removed, if specified, a pointwise inner iteration flux convergence criteria is used instead of the integral test, the integral inner iteration convergence criteria specifies that the average absolute pointwise flux error be less than epsilon, input data is processed by the FIDO routine used in DTF-II and ANISN, and, if the linear difference equations produce a negative flux, the flux is recalculated using the step function difference equations. This technique, which inhibits oscillation due to extrapolation, is optional.

6. RESTRICTIONS OR LIMITATIONS

Problem size is limited by machine size.

7. TYPICAL RUNNING TIME

No statistics have been accumulated by RSIC as to typical running time.

8. COMPUTER HARDWARE REQUIREMENTS

Standard equipment is used on either computer, and a maximum of 7 tapes or direct access devices in addition to I-O is utilized.

9. COMPUTER SOFTWARE REQUIREMENTS

The packaged codes were run on the IBM 7090/7094 IBSYS Operating System using IBJOB Processor, on the IBM 360/75 Operating System using OS-360 Fortran G and H Compiler, or on the CDC-6600.

10. REFERENCES

F. R. Mynatt, A User's Manual for DOT, K-1694 (January 1967).

F. R. Mynatt, F. J. Muckenthaler, and P. N. Stevens, Development of Two- Dimensional Discrete Ordinates Transport Theory for Radiation Shielding, CTC-INF- 952 (August 1969).

Duaine Lindstrom, DASH FORTRAN IV Void Tracing and SN-Monte Carlo Bridging Code, Aerojet Nuclear Systems Company SRT-TRM01-W393-4C (May 1970).

D. G. Lindstrom (Aerojet-General) and J. H. Price (Radiation Research Associates), Coupled Discrete Ordinates Monte Carlo Technique and Application to NERVA, AGC-NRO 1373 (1969).

R. G. Soltesz and R. K. Disney, User's Manual for the DOT-II W Discrete Ordinates Transport Computer Code, WANL-TME-1982 (December 1969).

R. G. Soltesz, R. K. Disney, J. Jedruch, and S. L. Ziegler, User's Manual for the DOT-II W Discrete Ordinates Transport Computer Code, WANL-TME-1982 Revision A (September 1970).

R. G. Soltesz and R. K. Disney, DOQ and ADOQ Discrete Ordinates Quadrature Codes Manual, WANL NRD-68-718 (November 1968).

R. K. Disney, GAMLEG User's Manual, WANL NRD-69-172 (May 1969).

G. Collier and R. Roth (CDC), An Assembly Language Version of GRIND for the CDC 6600 Computer, WANL-TME-1809 (June 1968).

Larry L. Moran and Richard G. Soltesz, FLUXPLT, A FORTRAN IV Program to Plot Isoflux Lines Based on the Scalar Flux Calculated by the DOT Program, WANL- TME-1813 (June 1968).

P. A. Read, W. E. Selph, and R. J. Cerbone, DUCT Code Manual, Gulf-RT-10654 (April 1971).

11. CONTENTS OF CODE PACKAGE

Included are the referenced documents and a reel of magnetic tape which contains the source codes, data, and input for sample problems written in BCD/EBCDIC card images and out put listing from running the problems; total records 22,689.

12. DATE OF ABSTRACT

May 1969; updated July 1981.

KEYWORDS: DISCRETE ORDINATES; NEUTRON; GAMMA-RAY; TWO- DIMENSIONS; MULTIGROUP; OBSOLETE