**1. NAME AND TITLE**

TWOTRAN-SPHERE: Multigroup Two-Dimensional Discrete Ordinates Transport Code
System in Spherical Geometry.

TWOTRAN-SPHERE is one in a code series developed at Los Alamos National Laboratory.
Others packaged in the TWOTRAN series are CCC-195/TWOTRAN and CCC-222/TWOTRAN
II.

**2. CONTRIBUTOR**

Los Alamos National Laboratory, Los Alamos, New Mexico.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; CDC 6600.

**4. NATURE OF PROBLEM SOLVED**

TWOTRAN-SPHERE is a modification of general-geometry TWOTRAN to solve two
dimensional particle transport problems in R-O spherical geometry. Both direct and adjoint,
homogeneous 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**

Finite difference techniques peculiar to the solution of the Boltzmann transport equation in two-dimensional spherical geometry are utilized.

TWOTRAN-SPHERE operates just as does the general geometry TWOTRAN with the
following major differences: 1) TWOTRAN-SPHERE uses a separable Legendre-Chebyshev
quadrature with MM = (ISN**2)/4 points per octant; 2) Geometric functions calculated are
different; 3) New angular coefficients and a new angular flux array are required in TWOTRAN-SPHERE; 4) Area and volume elements are retained as two-dimensional arrays in TWOTRAN-SPHERE; 5) Solution procedures are revised to allow for the computation of the extra angular flux
and other special procedures; and 6) A special edit is allowed. In TWOTRAN-SPHERE, the
normal edit of the general geometry TWOTRAN is augmented by a special edit, used only in
adjoint calculations. The edit allows the evaluation of an integral which depends parametrically on
an angle and the further energy integration of the integral over several source spectra. In the edit it
is assumed that a full-sphere combination has been made.

**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 LENXCA can be used. For
a 65K machine LENXCA can be greater than 35,000, depending on local system requirements.
With a few exceptions, only within group problem data are stored in fast memory and 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 for TWOTRAN-SPHERE.

**8. COMPUTER HARDWARE REQUIREMENTS**

The code was designed for the CDC 6600.

**9. COMPUTER SOFTWARE REQUIREMENTS**

FORTRAN IV is used with a small amount of mixed integer-floating arithmetic, generalized
subscripting, encode statements, and minor use of 10 H Hollerith formats.

**10. REFERENCES**

K. D. Lathrop and F. W. Brinkley, "TWOTRAN-SPHERE: A FORTRAN Program to Solve the Multigroup Transport Equation in Two Dimensional Spherical Geometry," LA-4567 (November 1970).

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**

August 1971; revised December 1984.

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