**1. NAME AND TITLE**

TRANZIT: Multigroup Time-Dependent Discrete Ordinates Radiation Transport Code System in (rho,z) Cylindrical Geometry.

**2. CONTRIBUTOR**

Los Alamos Scientific Laboratory, Los Alamos, New Mexico.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; CDC 7600 and CDC 6600.

**4. NATURE OF PROBLEM SOLVED**

TRANZIT solves multigroup time-dependent particle transport problems in finite rho,z cylindrical geometry. Problems solved are subject to a variety of boundary conditions including albedos and specification of the incoming angular flux at the right, top, or bottom of the cylinder. A time-dependent, anisotropic, inhomogeneous, distributed source that is separable in space-time may be used. No provision is made for including a fission source. A first collision source due to an energy-distributed point source on the axis of a system with material properties non-uniform in the z-direction is treated. General anisotropic scattering problems are treated.

Unusual features include coarse mesh convergence acceleration, first collision source option,
input specification of top, bottom, or right boundary fluxes, fine mesh z-dependence of cross
sections, a variety of boundary conditions, generalized anisotropic scattering and anisotropic
inhomogeneous source option, built-in discrete ordinates constants (S_{2}, S_{4},...S_{16}), and FIDO cross
section input option.

**5. METHOD OF SOLUTION**

Energy dependence is treated by the multigroup approximation and angular dependence by a discrete ordinates approximation. The space-time variables are approximated by the weighted-diamond difference scheme. Anisotropic scattering and anisotropic inhomogeneous sources are represented by finite spherical harmonics expansions. A first collision source option evaluates the analytic uncollided flux due to a point source on the cylinder axis in a medium which may have z-dependent cross sections, and uses this flux to compute a first collision source for further transport. Time differencing is also variable between the Crank-Nicholson (diamond) and completely implicit (step) schemes. The resulting scheme is stable and can be accurate but requires within-group iteration at each time step. Coarse-mesh rebalancing acceleration of these within-group iterations is performed.

**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 of less than MAX can be used. This is slightly greater than 25,000 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 storage and current angular flux is stored on disk. Arbitrary numbers of groups of up or down scattering are allowed.

**7. TYPICAL RUNNING TIME**

A ten group, S_{6}, P_{2} scattering, 28 x 40, first collision source problem ran 18 time steps per
hour on the CDC 7600. A three group, S_{4}, 4 x 6, up and down scattering, isotropic source and
scattering text problem required 0.3 minutes on the CDC 7600.

**8. COMPUTER HARDWARE REQUIREMENTS**

Six output units (disks, drums, or tapes) in addition to three system I-O 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**

FORTRAN IV with provision for mixed integer floating arithmetic, generalized subscripting, 10H Hollerith formats, decode, and encode statements.

**10. REFERENCE**

K. D. Lathrop, R. E. Anderson, F. W. Brinkley, "TRANZIT: A Program for Multigroup Time-Dependent Transport in (rho,z) Cylindrical Geometry," LA-4575 (December 1970).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document and one (1.2MB) DOS diskette which contains source program and sample problem input.

**12. DATE OF ABSTRACT**

September 1972; updated April 1975.

**KEYWORDS: ** DISCRETE ORDINATES; TIME-DEPENDENT; TWO-DIMENSIONS;
CYLINDRICAL GEOMETRY; NEUTRON; GAMMA-RAY