**1. NAME AND TITLE**

ONETRAN: A One-Dimensional Multigroup Discrete Ordinates Finite Element Transport Code System.

**2. CONTRIBUTOR**

Los Alamos National Laboratory, Los Alamos, New Mexico.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; CDC 7600 (A), IBM 360/370/3033 (B), CRAY (C).

**4. NATURE OF PROBLEM SOLVED**

ONETRAN solves the one-dimensional multigroup transport equation in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous (keff and eigenvalue searches) problems subject to vacuum, reflective, periodic, white, albedo, or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted.

**5. METHOD OF SOLUTION**

The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. Negative fluxes are eliminated by a local set-to-zero and correct algorithm. Standard inner (within-group) iteration cycles are accelerated by system rebalance, coarse-mesh rebalance, or Chebyshev acceleration. Outer iteration cycles are accelerated by coarse-mesh rebalance.

**6. RESTRICTIONS OR LIMITATIONS**

Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. On CDC machines MAXCOR can be about 25,000 words and peripheral storage is used for most group-dependent data.

**7. TYPICAL RUNNING TIME**

A 6-group, 106-interval mesh, S_{2} k_{eff} calculation with four outer iterations of an EBR-II core
requires 7.5 s on the CDC 7600. A 20-group, 134-interval mesh, S_{4} k_{eff} cell calculation with 12
outer iterations requires 5.5 min on the CDC 7600.

**8. COMPUTER HARDWARE REQUIREMENTS**

ONETRAN is operable on the CDC 7600 (A) IBM 3033 (B), and CRAY (C) computers. Five interface units (use of interface units is optional), five output units, and two system input/output units are required. A large bulk memory is desirable, but may be replaced by disk, drum, or tape storage.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A FORTRAN IV compiler is required.

**10. REFERENCES**

T. R. Hill, "ONETRAN Manual Errata" (June 1975).

T. R. Hill, "ONETRAN, A Discrete Ordinates Finite Element Code for the Solution of the One-Dimensional Multigroup Transport Equation," LA-5990-MS (June 1975).

Informal Notes on Input Modifications for CRAY Version, LANL (October 1982).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced documents and one (1.2MB) DOS diskette which contains the source code plus sample problem input and output.

**12. DATE OF ABSTRACT**

October 1978; revised March 1982, January 1983, November 1983, and April 1990.

**KEYWORDS: ** ONE-DIMENSION; MULTIGROUP; DISCRETE ORDINATES;
CYLINDRICAL GEOMETRY; SLAB; SPHERICAL GEOMETRY; FINITE
ELEMENT METHOD; NEUTRON; GAMMA-RAY