**RSICC CODE PACKAGE CCC-709**

**1. NAME AND TITLE**

TDTORT: Time-Dependent, Three-Dimensional, Discrete Ordinates, Neutron
Transport Code System.

**AUXILIARY ROUTINES**

GIP: Group cross-section preparation.

**2. CONTRIBUTORS**

The University of Tennessee, Nuclear Engineering Department, Knoxville, Tennessee.

Oak Ridge National Laboratory, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

Fortran 77 and C; SUN Ultra; DEC OSF/1, PC under Linux (C00709/MNYWS/00).

4**. NATURE OF PROBLEM SOLVED**

TDTORT solves the time-dependent, three-dimensional neutron transport equation with explicit representation of delayed neutrons to estimate the fission yield from fissionable material transients. This release includes a modified version of TORT from the C00650MFMWS01 DOORS3.1 code package plus the time-dependent TDTORT code. GIP is also included for cross-section preparation.

TORT calculates the flux or fluence of particles due to particles incident upon the system from extraneous sources or generated internally as a result of interaction with the system in two- or three-dimensional geometric systems. The principle application is to the deep-penetration transport of neutrons and photons. Reactor eigenvalue problems can also be solved. Numerous printed edits of the results are available, and results can be transferred to output files for subsequent analysis.

TDTORT reads ANISN-format cross-section libraries, which are not included
in the package. Users may choose from several available in RSICC's data
library collection which can be identified by the keyword "ANISN FORMAT."

**5. METHOD OF SOLUTION**

The time-dependent spatial flux is expressed as a product of a space-, energy-, and angle-dependent shape function, which is usually slowly varying in time and a purely time-dependent amplitude function. The shape equation is solved for the shape using TORT; and the result is used to calculate the point kinetics parameters (e.g., reactivity) by using their inner product definitions, which are then used to solve the time-dependent amplitude and precursor equations. The amplitude function is calculated by solving the kinetics equations using the LSODE solver. When a new shape calculation is needed, the flux is calculated using the newly computed amplitude function.

The Boltzmann transport equation is solved using the method of discrete ordinates to treat the directional variable and weighted finite-difference methods, in addition to Linear Nodal and Linear Characteristic methods in TORT to treat spatial variables. Energy dependence is treated using a multigroup formulation. Starting in one corner of a mesh, at the highest energy, and with starting guesses for implicit sources, boundary conditions and recursion relationships are used to sweep into the mesh for each discrete direction independently. Integral quantities such as scalar flux are obtained from weighted sums of the directional results. The calculation then proceeds to lower energy groups, one at a time.

Iterations are used to resolve implicitness caused by scattering between
directions within a single energy group, by scattering from an energy group
to another group previously calculated, by fission, and by certain types
of boundary conditions. Methods are available to accelerate
convergence
of both inner and outer iterations. Anisotropic scattering is represented
by a Legendre expansion of arbitrary order, and methods are available to
mitigate the effect of negative scattering source estimates resulting from
finite truncation of the expansion. Direction sets can be biased, concentrating
work into directions of particular interest. Fixed sources can be specified
at either external or internal mesh boundaries, or distributed within mesh
cells.

**6. RESTRICTIONS OR LIMITATIONS**

TORT's limitations for solving a three-dimensional, fixed source problem
apply (i.e., geometry, convergence, non-linear effects, etc.). External
forces and nonlinear physical effects cannot be treated. Penetration through
large, non-scattering regions may become inaccurate due to ray effects.
Problems with scattering ratios near unity or eigenvalue calculations with
closely spaced eigenvalues may be quite time-consuming. Although flexible
dimensioning is used in TORT so that no fixed limits on group, problem
size, etc., are applicable, TDTORT uses a fixed size container array, which
may not be big enough for very large problems. The user should change the
value of isdim in comsd3.F and recompile. When the size is not sufficient,
the code will indicate how much it needs (which can be used to determine
the new size).

**7. TYPICAL RUNNING TIME**

Running time is roughly proportional to the number of fixed source (flux
update) calculations each being proportional to mesh cells, directions,
groups, and iterations. The codes compiled in only a few minutes. Test
cases ran in about 47 minutes on a Sun UltraSparc 60, in 19 minutes on
a DEC, and in 18 minutes on Pentium III 450Mhz computer.

**8. COMPUTER HARDWARE REQUIREMENTS**

TDTORT was developed on Sun workstations. It was compiled, and test
cases were run on DEC Alpha Digital Unix workstations and personal computers
under Linux.

**9. COMPUTER SOFTWARE REQUIREMENTS**

The codes run under Unix or Linux. Fortran and C compilers are required for installation on Unix systems. Executables created with the Portland Group Inc. Workstation 3.3 f77 compiler are included for Linux users. TDTORT was tested at RSICC on the following systems:

Sun SparcStation 60, OS5.6, SUN Fortran 77 Ver 5

DEC 500au, Digital UNIX 4.00, Digital Fortran 77 Version 5.6-075

Pentium III 450Mhz under RedHat Linux 6+ with PGI Workstation 3.3 f77

**10. REFERENCES**

**a. included in hardcopy form:**

Sedat Goluoglu, "A Deterministic Method for Transient, Three-Dimensional
Neutron Transport," Ph.D. Dissertation, Nuclear Engineering Department,
The University of Tennessee, Knoxville (August 1997).

**b. included in electronic pdf format:**

W. A. Rhoades and D. B. Simpson, "The TORT Three-Dimensional Discrete
Ordinates Neutron/Photon Transport Code," ORNL/TM-13221 (October 1997).

W. A. Rhoades and M. B. Emmett, the GIP section of "DOS: The Discrete
Ordinates System," ORNL/TM-8362 (September 1982).

**c. background information:**

S. Goluoglu, H.L. Dodds, "A Time-Dependent, Three-Dimensional Neutron
Transport Methodology," *Nucl. Sci. Eng., 139, 248-261* (2001).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced documents and a GNU compressed Unix tar
file on CD. The tar file contains the source files for TDTORT, TORT, and
GIP, plus Linux executables, test cases, information file, and scripts.

**12. DATE OF ABSTRACT**

March 2002.

**KEYWORDS:** DISCRETE ORDINATES; NEUTRON; GAMMA-RAY; MULTIGROUP;
ADJOINT; SPHERICAL GEOMETRY; SLAB; CYLINDRICAL GEOMETRY; COMPLEX GEOMETRY;
KINETICS; TIME-DEPENDENT; WORKSTATION