**1. NAME AND TITLE**

DIXY-2**: **2-D Homogeneous and Inhomogeneous
Neutron Diffusion N X-Z, R-Z, R-Theta Geometry with Perturbation.

**2. CONTRIBUTOR**

Institut
fur Neutronenphysik and Reaktortechnik, Kernforschungszentrum Karlsruhe, Germany through the OECD Nuclear Energy Agency Data Bank, Issy-les-Moulineaux, France.

**3. CODING LANGUAGE
AND COMPUTER**

Fortran IV; IBM 370 Series (C00812I037000).

**4. NATURE OF
PROBLEM SOLVED**

The multigroup neutron diffusion equations are solved for two-dimensional x-y, r-z and r-theta geometries in the homogeneous or inhomogeneous case.

This programme supersedes the former DIXY programme, which is a part of the Karlsruhe Nuclear Program system NUSYS. An improved version of DIXY-2 has been implemented within the Karlsruhe Modular System KAPROS since 1974.

**5. METHOD OF
SOLUTION**

The analytical equations are approximated by five-point difference formulas and the resulting numerical problem is solved by an inner-outer iteration technique, where inner iterations are performed along a cyclically reduced block over relaxation with pre-calculated relaxation factors. The following conditions are permissible in the utilization of the code:

a)
Three outer boundary conditions may be imposed - zero flux, zero current or
constant current/flux.

b) Inner boundary conditions may be used for rod calculations.

c) Normal and adjoint eigenvalue problems, fixed source and criticality search
problems are solved.

d) Scattering down from any group to any other is allowed.

e) Included is a perpturbation part for r-z geometry and a routine for calculating
any reaction rates or densities.

f) Subsequent cases can be queued in one job step.

g) Automatic source interpolation within subsequent cases to reduce calculation
time.

h) Time-eigenvalue calculation.

i) Calculation of dynamical neutron life time.

j) Calculation of beta-effective.

k) Included in DIXY-2 is a subroutine that prints out an input description if
the program is started with only one input card, containing the character
string 'DESCRIPTION', punched from card column 1 (apostrophes omitted).

l) DIXY-2 contains a plot facility.

m) Space-energy dependent fixed source problems.

n) Directionally dependent diffusion coefficients may be specified for
streaming problems.

**6. RESTRICTIONS OR
LIMITATIONS**

The maximum number of mesh points and/or groups depends on the available core storage in the following manner. Assume:

C = total number of available core storage words

P = program length in words

NGP = number of groups

NM = number of material compositions

MXN = number of mesh points

Q = NM*NGP*(NGP+5)/2 - approximate store for cross sections then:

C.GE.(P+Q+S+4.5*MXN) must be true.

If this relation holds, the program searches for an optimal way to solve the problem with a minimum number of I/O devices (max. 2) using the adjustable dimension feature.

**7. TYPICAL RUNNING
TIME**

13*G seconds for a problem with 1000 mesh points and G groups on an IBM 370/168 at a source accuracy of 0.001.

**8. COMPUTER
HARDWARE REQUIREMENTS**

IBM 360 or IBM 370 mainframe.

A maximum of 2 tape drives or one disc pack is required.

**9. COMPUTER
SOFTWARE REQUIREMENTS**

IBM 360/OS.

**10. REFERENCES**

**a) Included Documentation**

W. Hoebel, “Numerical Methods Used in the Two-Dimensional Neutron Diffusion Program DIXY,” Kernforschungszentrum Karlsuhe, Institut fur Neutronenhysik und Reaktortechnik, Postfach 340, 2-7500 Karlshrue, Federal Republic of Germany.

**11. CONTENTS OF CODE
PACKAGE**

The package is distributed on a CD with a compressed zip file including source files, JCL, documentation and sample data and output.

**12. DATE OF ABSTRACT**

November 2013.

**KEYWORDS: **EIGENVALUES,
ITERATIVE METHODS, MULTIGROUP, NEUTRON DIFFUSION EQUATION, R-THETA, R-Z,
TWO-DIMENSIONAL, X-Y