**1. NAME AND TITLE**

TRIGON: Two-Dimensional Multigroup Diffusion Code SystemTrigonal or Hexagonal
Mesh.

**2. CONTRIBUTOR**

Nuclear Engineering Laboratory, Technical Research Centre of Finland, Helsinki, Finland.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN V; UNIVAC 1108.

**4. NATURE OF PROBLEM SOLVED**

TRIGON solves the multigroup time-independent neutron diffusion equations with arbitrary
group-to-group scattering in two space dimensions. In addition to homogeneous or k-effective
calculations, inhomogeneous or fixed source calculations can be made. The problem may be
specified with both external and internal logarithmic derivative boundary conditions. Using the
pointwise flux distribution, the program automatically calculates the average flux and power
distributions over equal hexagons of arbitrary size into which the area of solution is divided by the
user.

**5. METHOD OF SOLUTION**

The diffusion theory equations are approximated by 7-point difference equations for the
uniform triangular or hexagonal mesh grid. In the former case, the mesh points are situated at the
cross-sections of the mesh lines separating different materials and in the latter case at the center
points of the homogeneous mesh hexagons. The difference equations are solved iteratively by the
line over-relaxation technique utilizing an exponential over-relaxation procedure. Coarse mesh
rebalancing and special asymptotic flux extrapolation are used to improve the convergence.

**6. RESTRICTIONS OR LIMITATIONS**

Due to variable dimensioning of arrays, the only restriction on problem size is the available
core storage. The program requires about 27,000 words on the UNIVAC 1108. This can be
reduced to less than 15,000 words by segmentation. In addition, a minimum of approximately
10,000 words must be available for variable dimensioned arrays.

**7. TYPICAL RUNNING TIME**

The basic running time is about 0.2 minutes per space-energy point per iteration when the calculation is performed entirely within the core storage. Usually, some 100 iterations will be enough for convergence.

If the problem involves the use of auxiliary storage devices (tapes, discs, or drums) during the
calculation, the running time will be increased due to the fact that computation and data transfer are
not performed simultaneously.

**8. COMPUTER HARDWARE REQUIREMENTS**

TRIGON is designed to operate on a UNIVAC 1108 computer with 64 K words of core
storage. A maximum of six auxiliary files will be used. These can be either tape, disc, or drum
files. The clock is sampled.

**9. COMPUTER SOFTWARE REQUIREMENTS**

TRIGON was designed for the EXEC-8 operating system. The UNIVAC 1108 library routine
NTRAN is used to perform unbuffered data transfer between core storage and auxiliary files. The
CLOCK routine requires Assembly Language.

**10. REFERENCE**

E. Kaloinen, "TRIGON, A Two-Dimensional Multigroup Diffusion Code for Triagonal or
Hexagonal Mesh," Technical Research Centre of Finland, Nuclear Engineering Laboratory, VTT-YDI-1 (May 1973).

**11. CONTENTS OF CODE PACKAGE**

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

**12. DATE OF ABSTRACT**

December 1981.

**KEYWORDS: ** TWO-DIMENSIONS; MULTIGROUP; DIFFUSION THEORY; NEUTRON