** RSICC
CODE PACKAGE CCC-695**

**1. NAME
AND TITLE**

SUSD3D: A Multi-Dimensional, Discrete-Ordinates Based Cross Section Sensitivity and Uncertainty Analysis Code System.

**Auxiliary Routines:**

NJOY-SUSD3D (SUNJOY): Nuclear data processing code based on NJOY system, including the modules ERR34, GROUPS and SEADR.

**2. CONTRIBUTORS**

Institute Jozef Stefan , Slovenia, through the OECD NEA Data Bank, Issy‑les‑Moulineaux, France.

**3. CODING
LANGUAGE AND COMPUTERS**

Fortran 95; PC Linux (C00695MNYCP01).

**4. NATURE
OF PROBLEM SOLVED**

SUSD3D 2008 calculates sensitivity coefficients and standard deviation in the calculated detector responses or design parameters of interest due to input cross sections and their uncertainties. One-, two- and three-dimensional transport problems can be studied. Several types of uncertainties can be considered, i.e. those due to (1) neutron/gamma multi-group cross sections, (2) energy-dependent response functions, (3) secondary angular distribution (SAD) or secondary energy distribution (SED) uncertainties.

SUSD3D, initially released in 2000, is loosely based on the SUSD code by K. Furuta, Y. Oka and S. Kondo from the University of Tokyo in Japan. SUSD 2008 modifications are primarily relevant for the sensitivity calculations of the critical systems and include:

o Correction of the sensitivity calculation for prompt fission and number of delayed neutrons per fission (MT=18 and MT=455).

o An option allows the re-normalization of the prompt fission spectra covariance matrices to be applied via the "normalization" of the sensitivity profiles. This option is useful in case if the fission spectra covariances (MF=35) used do not comply with the ENDF-6 Format Manual rules.

o For the criticality calculations the normalization can be calculated by the code SUSD3D internally. Parameter NORM should be set to 0 in this case. Total number of neutrons per fission (MT=452) sensitivities for all the fissile materials must be requested in the SUSD3D OVERLAY-2 input deck in order to allow the correct normalization.

o The cross section data format reading was updated, mostly for critical systems (e.g. MT18 reaction).

o Fission spectra uncertainties can be calculated using the file MF35 data processed by the ERROR-J code.

o Cross sections can be input directly using input card "xs" (vector data only).

o k-eff card was added for subcritical systems.

o This version of SUSD3D code is compatible with the single precision DANTSYS code package (CCC-0547/07 and /08, which are the latest versions available from NEA-DB).

o The memory and data management was updated as well as the language level (code was rewritten from Fortran-77 to Fortran-95).

SUSD3D is coupled to several discrete‑ordinates codes via binary interface files. SUSD3D can use the flux moment files produced by discrete ordinates codes: ANISN, DORT, TORT, ONEDANT, TWODANT, and THREEDANT. In some of these codes minor modifications are required. Variable dimensions used in the TORT‑DORT system are supported. In 3D analysis the geometry and material composition is taken directly from the TORT produced VARSCL binary file, reducing in this way the user's input to SUSD3D.

Multigroup cross‑section sets are read in the GENDF format of the NJOY/GROUPR code system, and the covariance data are expected in the COVFIL format of NJOY/ERRORR or the COVERX format of PUFF‑2.

The ZZ‑VITAMIN‑J/COVA cross section covariance matrix library can be used as an alternative to the NJOY code system. The package includes the ANGELO code to produce the covariance data in the required energy structure in the COVFIL format.

The following cross section processing modules to be added to the NJOY‑94 code system are included in the package:

o ERR34: an extension of the ERRORR module of the NJOY code system for the File‑34 processing. It is used to prepare multigroup SAD cross sections covariance matrices.

o GROUPSR: An additional code module for the preparation of partial cross sections for SAD sensitivity analysis. Updated version of the same code from SUSD, extended to the ENDF‑6 format.

o SEADR: An additional code module to prepare group covariance matrices for SAD/SED uncertainty analysis.

** **

**5. METHOD
OF SOLUTION**

First-order perturbation theory is used to obtain sensitivity coefficients. They are derived from the direct and adjoint flux moments (or angular fluxes) calculated by the discrete ordinates codes listed above. The sensitivity profiles are folded with the cross section covariance matrices to determine the variance and standard deviation in an integral response of interest.

** **

**6.
RESTRICTIONS OR LIMITATIONS**

Variable dimensioning is used providing flexibility to adjust the storage requirements. Core storage is reserved for a particular dimensional array only during the time the corresponding data are needed in the calculation, afterwards the array is released for other data.

**7.
TYPICAL RUNNING TIME**

Highly problem dependent, running time is affected by the parameters like the number of energy groups, number of dimensions (1, 2, 3), number of spatial intervals and PN approximation order used in the discrete ordinates transport calculations. The most complex case studied (VENUS-3 benchmark analysis based on TORT 3D calculation using P-3/S-8 and 51/52/22 X/Y/Z intervals) took 2 hours 40 minutes on a PC Pentium.

**8.
COMPUTER HARDWARE REQUIREMENTS**

SUSD3D runs on Unix workstations and on personal computers. Core requirements depend on problem complexity. Up to 8 disks or tape devices are required in addition to the standard input and output devices.

**9.
COMPUTER SOFTWARE REQUIREMENTS**

A Fortran compiler is required; no executables are included in the package. The developer has run SUSD3D under RedHat Linux 7.2 using the Lahey/Fujitsu Fortran 95 Linux PRO version 6.1 compiler. At RSICC, it was tested under RedHat Enterprise Linux 4 with the Intel 9.1 Fortran compiler. Earlier releases ran under other Unix operating systems and Windows. It is expected that this version can be run on these systems.

** **

**10.
REFERENCES**

**a) included in documentation**:

I. Kodeli, “SUSD3D - 2008, A Multi-Dimensional, Discrete Ordinates based Cross Section Sensitivity and Uncertainty Code” (January 2008).

B. Zefran, “Upgrading the Sensitivity/Uncertainty Analysis code system SUSD-3D concerning memory and data management and language level (from Fortran-77 to Fortran-95)” (January 2005).

**b) background information**:

K. Furuta, Y. Oka, S. Kondo, “SUSD: A Computer Code for Cross‑Section Sensitivity and Uncertainty Analysis Including Secondary Neutron Energy and Angular Distributions,” from University of Tokyo in Japan, ORNL/TR-88/18 (1988); RSICC package was CCC-501.

I. Kodeli, “SUSD3D, A Multi-Dimensional, Discrete Ordinates Based Cross Section Sensitivity and Uncertainty Code,” Proc. PHYSOR-2000, Pittsburgh, PA (May 2000).

I. Kodeli, “Cross-Section Data Uncertainty and How Such Information is Used in Fusion Analysis,” presented at the Reg. Meeting on Nuclear Energy in Central Europe, Portoro Solvenia (Sept. 7-10, 1999).

I. Kodeli, “Progress on Computational Tools for 3D Sensitivity and Uncertainty Analsyis,” OCED-NEA Seminar on 3D Deterministic Radiation Transport Computer Programs Features, Applications and Perspectives, Paris (2-3 Dec. 1996).

I. Kodeli, “Analysis of VENUS-3 Benchmark Experiment,” Proc. Reg. Meeting on Nuclear Energy in Central Europe, Solvenia (Sept. 7-10, 1998).

W. A. Rhoades, R. L. Childs, “TORT‑DORT: Two‑ and Three‑Dimensional Discrete Ordinates Transport, Version 2.7.3,” ORNL, RSIC CCC-543 replaced by CCC-650 (1993) .

R. E. Alcouffe et al., “DANTSYS 3.0 ‑ A Diffusion‑Accelerated, Neutral‑Particle Transport Code System,” LA‑12969‑M, LANL, RSIC CCC-547 (1995).

W. W. Engle, “A User's Manual for ANISN, A One‑Dimensional Discrete Ordinates Transport Code with Anisotropic Scattering,” K-1693 ORNL (1967).

R. E. MacFarlane, D. W. Muir, “The NJOY Nuclear Data Processing System,” Manual LA‑12740‑M RSIC PSR-355 (1994).

**11.
CONTENTS OF CODE PACKAGE**

Included are the referenced document in (10.a), source code, and test problems, which are transmitted on a CD in GNU compressed Unix tar file. No executables are included with the package.

** **

**12. DATE
OF ABSTRACT**

October 2000, revised May 2008.

**KEYWORDS:** DISCRETE
ORDINATES; MULTIGROUP; NEUTRON; SENSITIVITY ANALYSIS; PERTURBATION THEORY