**1. NAME AND TITLE**

TWOTRAN (BASIC, PN, FC, VW, PNVW): Two-Dimensional Discrete Ordinates Code
System with Spherical Harmonics, First Collision Course, and Variable Weight Options.

**AUXILIARY ROUTINES**

TWOTRAN-BASIC: General Purpose Two-Dimensional Transport Basic Code.

TWOTRAN-PN: Spherical Harmonics Version.

TWOTRAN-FC: First Collision Source Version.

TWOTRAN-VW: Variable Weight Version.

TWOTRAN-PNVW: Spherical Harmonics Variable Weighted Version.

**2. CONTRIBUTOR**

Los Alamos National Laboratory, Los Alamos, New Mexico.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; CDC 6600 and 7600.

**4. NATURE OF PROBLEM SOLVED**

TWOTRAN is designed to solve the multigroup discrete ordinates approximation to the two-dimensional Boltzmann equation for particle transport problems in x-y, r-z and r-theta geometries.
Three special versions allow for new methods by using the major parts of TWOTRAN-BASIC.
Both direct and adjoint, homogeneous (k_{eff} or parametric eigenvalue searches) or inhomogeneous
time-independent problems are solved subject to vacuum, reflective, white, periodic, or input
specification of boundary flux conditions. Both anisotropic inhomogeneous problems and general
anisotropic scattering problems are treated. Arbitrary numbers of groups of up- or down-scattering
are allowed.

**5. METHOD OF SOLUTION**

The LANL general-geometry TWOTRAN is the basic two-dimensional transport code designed for ease in alteration for use in conjunction with three special versions employing new methods. The first of these versions, TWOTRAN-PN, is designed to solve discrete ordinates equations that have been converted to equations like spherical harmonics equations to eliminate ray effects. TWOTRAN-FC computes the analytic flux due to a point source on the axis of a finite cylinder and automatically uses this flux to compute the first collision source of particles for further transport. TWOTRAN-VW uses a variable weight diamond difference scheme for calculating spatial derivatives. TWOTRAN-PNVW is a spherical harmonics, variable weighted version with optional spherical harmonic or discrete ordinate solution. All operate from TWOTRAN-BASIC and offer the options available in it for three two-dimensional geometries.

Energy dependence is treated by the multigroup approximation and the angular dependence by
a discrete ordinates approximation. Space dependence is approximated by the diamond difference
scheme with a set-to-zero negative flux control. Anisotropic scattering and anisotropic inhomogeneous sources are represented by finite spherical harmonics expansions. Within-group iterations,
upscattering iterations, k_{eff} iterations, and eigenvalue search iterations are accelerated by a coarse-mesh particle rebalancing algorithm. Unusual features include coarse-mesh convergence acceleration; coarse-mesh spatial and angular organization to permit larger problems; general anisotropic
scattering and inhomogeneous source option; input specification of top, bottom, or right boundary
fluxes; built-in discrete-ordinates constants (S_{2}, S_{4} ..., S_{16}); diamond difference scheme with
negative flux fixup; detailed edit provisions; pointwise cross-section density variation option;
overlay program organization; general dump and restart options; and FIDO cross-section input
option.

**6. RESTRICTIONS OR LIMITATIONS**

The variable dimensioning capability of FORTRAN-IV is used so that any combination of
problem parameters leading to a blank common vector length less than MAXLEN can be used.
MAXLEN is slightly greater than 40,000 words for the CDC 7600. With a few exceptions, only
within-group problem data are stored in fast memory; data for all other groups are stored in
auxiliary bulk memory such as extended core storage.

**7. TYPICAL RUNNING TIME**

No study has been made by RSIC of typical running times using TWOTRAN-PNV. A one
group, S_{8} converted to P_{5}, isotropic problem with mesh size 20 x 20 ran in 0.2 minutes on the CDC
7600.

**8. COMPUTER HARDWARE REQUIREMENTS**

TWOTRAN-PNVW requires five output units (disk, drums or tapes) in addition to two system
input/output units. A CDC extended core storage unit or a large bulk memory is also required.
(Disk, drums or tapes can be substituted for this requirement.)

**9. COMPUTER SOFTWARE REQUIREMENTS**

TWOTRAN-PNVW is FORTRAN IV with a small amount of mixed integer-floating arithmetic
and generalized subscripting. There is minor use of 10 H Hollerith formats, decode and encode
statements. Double precision is used to calculate (but not to store) orthonormal polynomials. All
the versions are operable on CDC 7600 FORTRAN IV systems.

**10. REFERENCES**

K. D. Lathrop, F. W. Brinkley, and P. Rood, "Theory and Use of the Spherical Harmonics, First Collision Source, and Variable Weight Versions of the TWOTRAN Transport Program," LA-4600 (March 1972).

K. D. Lathrop and F. W. Brinkley, "Theory and Use of the General-Geometry TWOTRAN
Program," LA-4432 (May 1970).

**11. CONTENTS OF CODE PACKAGE**

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

**12. DATE OF ABSTRACT**

October 1975.

**KEYWORDS:** DISCRETE ORDINATES; NEUTRON; GAMMA-RAY; MULTIGROUP; TWO-DIMENSIONS; SPHERICAL HARMONICS