CCC-0726 CNCSN 2009.

1. NAME OR DESIGNATION OF PROGRAM:  CNCSN 2009

3. DESCRIPTION OF PROGRAM OR FUNCTION

KATRIN, KASKAD-S and ROZ-6 solve the multigroup transport equation for neutrons, photons and charged particles in 3D (x,y,z and r,theta,z), 2D (x,z, r,z and r,theta) and 1D (plane, spherical and cylindrical) geometries, respectively. The transport equation for charged particles can be solved with direct treatment of the continuous slowing-down (CSD) term; for 1D plane and spherical geometries the Boltzmann-Fokker-Plank equation can be solved with direct treatment both CSD and continuous scattering terms. The scattering anisotropy can be treated in the P2 approximation. The adjoint solution of the problem can be also obtained (for neutral particles only). The principal application is solving of deep-penetration transport problems, typical for radiation protection and shielding calculations. Fission problems (subcritical boundary value and keff), problems with upscattering (thermalization, etc), electron-photon and hadron cascade problems can be also solved.

A few standard types of reflecting boundary conditions can be used. Several types of boundary and volumetric sources, including point anisotropic source (for x,y,z, r,theta,z and r,z geometries), point and line isotropic sources for 1D spherical and cylindrical geometries, respectively (for neutral particles only); boundary monodirectional source (with given spatial distribution in the perpendicular section of the beam) that is normally incident on the bottom of x,y,z, r,theta,z and r,z geometry regions, plane monodirectional source, volumetric distributed isotropic source with factorized energy dependence and boundary both isotropic and anisotropic sources with factorized spatial dependence, have been implemented. In solving problems with fission the volumetric fission source file can be generated or used as input volumetric fission source file. When solving hadron cascade transport problems, the anisotropic spallation source file can be generated (or used as input anisotropic source file). It is important to note that meshes used for presentation of the sources are independent from the mesh used for approximation of transport equation.

BOT3P-5.1 mesh generator can be used as preprocessor. KASKAD-S and KATRIN codes can enter problem geometry from a file both in the 'matmap' and 'mixmap' format, defined in the BOT3P-5.1 code manual. In the 'matmap' format spatial zone dimensions, material map, spatial mesh and density factor are stored. In this case the original material mass conservation is supported globally for problem bodies. The 'mixmap' format stores the fine mesh boundary arrays, the material map distribution and the sequence of original material numbers, contained in meshes, where a few original materials are available, together with the related volume fractions for these meshes, so, the 'mixmap' format enables the material mass conservation locally. If geometry data are entered from a file in the 'mixmap' format then KASKAD-S and KATRIN codes generate additional mixtures, if required, to maintain the mass of original materials conservation for every spatial cell.

ConDat converter can also be used as a preprocessor. ConDat includes geometrical module NCG of Monte Carlo MCU transport code and is able to enter combinatorial geometry definition of problem geometry in terms of NCGSIM language used by NCG. MCU Viewer can be used to visualize and to test combinatorial geometry defined in terms of NCGSIM language that simplifies essentially preparing combinatorial geometry definition in solving real complicated geometry problems. To convert a combinatorial problem geometry form to a 'bit-mapped' one and generate the problem geometry file in the 'mixmap' format, ConDat code uses the tracing algorithm that is natural for geometrical module NCG of MCU code.

The possibility to calculate spectra/doses in a void outside KATRIN x,y,z and r,theta,z, and KASKAD-S  geometries is also implemented (for neutral particles only). Numerous printed edits of the results are available and output solution/source files can be written for subsequent analysis by postprocessors. Both KASKAD-S and KATRIN codes, and postprocessors KASF and KATRIF can generate the Atlas boundary files with the problem and material maps for given region section that can be used by SURFER to visualize the geometry entered before and (or) after transport calculation. A specially designed script is available to automate geometry visualization.

ARVES-2.5: cross-section preprocessor (package of utilities for operating with cross-section files in FMAC-M format). It includes utilities that can:

- perform interface: ANISN format (given in a binary or ASCII form) or GIP format (in a binary form) -> binary FMAC-M format;
- make listing and perform consistency tests of cross-sections in the FMAC-M format;
- cut unused groups;
- generate an adjoint cross-section file in FMAC-M format;
- transform the particle type organized group sequence in the coupled cross-section file to energy organized group sequence;
- transform the cross-section file with direct treatment of the CSD term to the file with indirect treatment of this term;
- collapse cross-sections prepared in the FMAC-M format by given spectra to a file with a smaller number of groups; and
- transform the binary form of the FMAC-M format to the ASCII one and vice verse.

MIXERM: utility for preparing mixtures with the use of binary cross-section libraries in ANISN format (with user-friendly input interface, similar to that used in CONSYST). The current version of MIXERM is applicable for BUGLE96, BGL1000, BGL440, and CASK coupled neutron and photon problem-dependent cross-section libraries.

CEPXS-BFP: adapted version of Sandia National Laboratory multigroup coupled electron-photon cross-section generating code CEPXS. The following new options, based on the "Monte-Carlo" option of CEPXS, have been implemented in CEPXS-BFP:

- "Sn-CSD" option. In this case the stopping power at group boundaries is available in the cross-section file generated. So, it is expected that Sn code used the CSD operator is treated directly, but the continuous-scattering operator is treated indirectly in the P2 approximation.

- "Sn-BFP" option. In this case both the stopping power at group boundaries and restricted momentum transfer are available in the cross-section file. So, it is expected that Sn code used both the CSD operator and continuous-scattering operator are treated directly.

- "Sn-indirect" is the last implemented new option. It is nearly identical with the standard option used by ONEDANT-LD, but the header cards have been changed to make one's more convenient for the use by the cross-section preprocessor ARVES-2.5 that transforms cross-section matrices prepared in ANISN format to FMAC-M format.

SADCO-2.4: Institute for High-Energy Physics modular system for generating coupled multigroup cross-sections for protons, pions, and neutrons in high-energy region (20 MeV < E < 10 GeV), coupled with standard coupled neutron/photon multigroup cross-sections below 20 MeV.

4. METHODS

The second-order of accuracy adaptive weighted diamond difference scheme (AWDD scheme) for spatial and angular variables is implemented. The AWDD scheme is also used for approximation of the continuous slowing-down term in solving charged particle transport problems. The fourth-order of accuracy linear moments/quadratic continuous (LM/QC) and third-order of accuracy linear discontinuous (LD) schemes in spatial variables are implemented for 1D and 2D x-z and r-z geometry case. A variant of the adaptive weighted LM/QC-weighted LD (AWLM/QC-WLD) scheme is available for 1D geometries case.

The P1 Synthetic Acceleration (P1SA) scheme for acceleration of inner iterations convergence, consistent with the WDD scheme, is implemented. For 1D geometries, the P1SA scheme for acceleration of inner iterations convergence, consistent with the WLM-WLD scheme, is available. The consistent P1SA scheme for acceleration of fission upscattering iterations convergence in solving subcritical problems and thermal upscattering iterations convergence with the use of the estimate by Fourier analysis spectrum shape function for homogenized problem is also implemented. For solving the P1SA system for acceleration corrections, the direct through-computations, iterative cyclic ADI and splitting-up methods are used in 1D, 2D and 3D geometries, respectively.

Parallelization of KATRIN code is performed via a 2-D spatial decomposition in x,y/r,theta transverse section of the problem geometry, which retains the ability to invert the source iteration equation in a single sweep (the KBA algorithm). Parallelization of KASKAD-S code is performed in a similar way via a 2-D spatial decomposition of x,z/r,z/r,theta regions. The solving of the P1 system for acceleration corrections is parallelized by performing the array of through-computation runs in parallel. Calculation of the scattering integral is also parallelized.

For point, linear and monodirectional sources, the unscattered component of the flux is selected and treated by analytical formulas. The codes work both with symmetrical and asymmetrical angular meshes. A module that generates suitable quadrature meshes (Esn type, Gauss-Chebychev and composite Sn type (the last quadrature can be used in the case when it is necessary to give more nodes in the desired angular direction)) is included in KATRIN. The number of discrete ordinates directions and the order of the P2 approximation can vary in energy groups.

To calculate spectra/doses in a void outside KATRIN or KASKAD-S geometry, the last-flight algorithm is implemented (for neutral particles only).

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The number of discrete ordinate directions, space intervals, energy groups, and the order of the scattering anisotropy approximation are limited only by the computer storage available through the use of dynamic storage allocation. All calculations in the PC-version of codes are performed with the double-precision arithmetic. The number of words needed for working arrays of the problem solved is available in the code abstracts.

6. TYPICAL RUNNING TIME

Run time for parallel multi-threaded version of codes essentially depends on number of threads available/used. It is also roughly proportional to the number of flux calculations: spatial mesh cells x directions x energy groups x iterations/group and depends on the order of the P2 approximation used. In solving 3D problems the run time essentially depends on the speed of external memory used. As an example, on Intel Core i7 920 PC, supplied by 12 Gb RAM and Windows Vista 64-bit, calculation of VVER-1200 radiation shield in r,theta,z geometry with by pin defined source, 218x120x175 = 4 578 000 spatial cells, 47 neutron and 20 photon energy groups of BGL1000 cross-section library in P1Sn approximation with point-wise convergence criterion of inner and upscattering iterations 10**-3 and 5x10**-3, respectively, by means of the AWDD scheme and the P1SA scheme for acceleration of both inner and up scattering iteration convergence requires 28 hours 38 min if the RAID 0 array of two WD "VelociRaptor" SATA-2 HD is used as a separate device for transport code working files. Calculation of a similar VVER-1200 radiation shield problem in r,z and r,theta geometries with 187x170 = 31 790 and 187x120 = 22 440 spatial cells, respectively, in P1Sn approximation with point-wise convergence criterion of inner and thermal up scattering iterations 10**-4 and 10**-3, respectively, requires 2 min 43 sec and 1 min 50 sec, respectively. The possibility to continue calculation after an interruption (needed in calculation of large variants) is also implemented in the transport codes included.

8. RELATED OR AUXILIARY PROGRAMS

AUXILIARY CODES included in the CNCSN package:
- KATRIN-2.5: Parallel multi-threaded three-dimensional neutral and charged particle transport.
- KATRIN-2.0: Serial three-dimensional neutral and charged particle transport.
- KASKAD-S-3.0: Parallel multi-threaded two-dimensional neutral and charged particle transport.
- KASKAD-S-2.5: Serial two-dimensional neutral and charged particle transport.
- ROZ-6.6: One-dimensional neutral and charged particle transport.
- ARVES-2.5: Preprocessor for the working macroscopic cross-section FMAC-M format for transport calculations.
- MIXERM: Utility for preparing mixtures on the base of multigroup cross-section libraries in ANISN format.
- CEPXS-BFP: A version of Sandia National Laboratory multigroup coupled electron-photon cross-section generating code CEPXS, adapted for solving the charged particle transport in the Boltzmann-Fokker-Planck formulation with the use of discrete ordinate method.
- SADCO-2.4: Institute for High-Energy Physics modular system for generating coupled nuclear data libraries to provide high-energy particle transport calculations by multigroup method.
- KATRIF: Postprocessor for KATRIN code.
- KASF: Postprocessor for KASKAD-S code.
- ROZ6F: Postprocessor for ROZ-6 code.
- ConDat 1.0: Code for converting by the tracing algorithm the combinatorial geometry presentation to the bit-mapped one.
- MCU Viewer: Code for combinatorial geometry visualization.
- Maplook: Script for SURFER to automate geometry visualization on the base of material maps given as atlas boundary (*.bna) files.
- SYNTH: Utility for construction of an approximate solution of 3D transport equation in vicinity of reactor pressure vessel by the synthesis method.

10. REFERENCES

Background references:
- L. P. Bass, A. M. Voloschenko and T. A. Germogenova, "Methods of Discrete Ordinates in Radiation Transport Problems," KIAM, Moscow (in Russian) (1986).
- A. M. Voloschenko, "Geometrical Interpretation of Family of Weighted Nodal Schemes and Adaptive Positive Approximations for Transport Equation," Proc. Joint International Conference on Mathematical Methods and Supercomputing for Nuclear Applications, Saratoga Springs, NY USA, vol. 2, p. 1517 (October 6-10, 1997).
- A. M. Voloschenko, "Experience in the Use of the Consistent  Synthetic Acceleration Scheme for Transport Equation in 2D Geometry," Proc. Of International Conference on Mathematics and Computations, Reactor Physics, and Environmental Analyses in Nuclear Applications, Madrid, Spain, vol. 1, p. 104 (27-30 September, 1999).
- A. M. Voloshchenko, "KP1 Acceleration Scheme for Inner Iterations Consistent with the Weighted Diamond Differencing Scheme for Transport Equation in Two-Dimensional Geometry," Computational Mathematics and Mathematical Physics, 41, No. 9, 1379 (2001).
- A. M. Voloschenko, "Consistent P1 Synthetic Acceleration Scheme for Transport Equation in 3D Geometries," Proc. of International Conference on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications, Avignon, France, on CD-ROM (September 12-15, 2005).
- A. M. Voloschenko et al., "The CNCSN: One, Two- and Three-Dimensional Coupled Neutral and Charged Particle Discrete Ordinates Code Package," Proc. Of International Conference on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications, Avignon, France, on CD-ROM (September 12-15, 2005).
- A. M. Voloschenko and S. V. Gukov, "Some New Algorithms for Solving the Coupled Electron-Photon Transport Problems by the Discrete-Ordinates Method," Proc. Int. Conf. On the New Frontiers of Nuclear Technology: Reactor Physics, Safety and High-Performance Computing - PHYSOR 2002, Seoul, Korea (October 7-10, 2002).
- D. V. Gorbatkov and V. P. Kryuchkov, "SADCO-2: A Modular Code System for Generating Coupled Nuclear Data Libraries to Provide High-Energy Particle Transport Calculation by Multigroup Methods," Nucl. Instr. & Meth. In Phys. Res., A 372, 297 (1996).
- R. Orsi, "BOT3P Version 5.1: A Pre/Post-Processor System for Transport Analysis," ENEA report FIS-P9H6-014, Italy (2006).
- M. I. Gurevich, D. S. Oleynik, A. A. Russkov and A. M. Voloschenko, "About the Use of the Monte-Carlo Code Based Tracing Algorithm and the Volume Fraction Method for Sn Full Core Calculations," Proc. of International Conference Advances in Nuclear Analysis and Simulation - PHYSOR 2006, Vancouver, Canada, on CD-ROM (September 10-14, 2006).
- L. P. Abagian et al., "MCU-REA/2 with Data Bank DLC/MCUDAT-2.2," Editors: E.A. Gomin, L.V. Maiorov. Report of RRC Kurchatov Institute No. 36/17-2006, Moscow
(2006).
- A. M. Voloschenko et al., "The CNCSN-2: One, Two- and Three-Dimensional Coupled Neutral and Charged Particle Discrete Ordinates Code System." Proc. Of International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics, Saratoga Springs, USA, May 3-7, 2009, on CD ROM.
- M. I. Gurevich et al. "Experience in the Use of the Monte-Carlo Code Based Tracing algorithm and the Volume Fraction Method in VVER Radiation Shielding Calculations," Proc. of International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics, Saratoga Springs, USA, May 3-7, 2009, on CD ROM.

- A. M. Voloschenko and A. A. Dubinin:
"ROZ-6.6 - One-Dimensional Discrete-Ordinates Neutron, Photon and Charged
Particles Transport Code," User's guide, Report of Keldysh Inst. of Appl.
Math., Russian Ac. of Sci., No. 7-25-2004, Moscow (2004).
- A. M. Voloschenko and A. V. Shwetsov:
"KASKAD-S-3.0 - Two-Dimensional Discrete-Ordinates Neutron, Photon and Charged
Particles Transport code," User's guide, Report of Keldysh Inst. of Appl.
Math., Russian Ac. of Sci., No. 7-26-2004, Moscow (2004).
- A. M. Voloschenko, V. P. Kryuchkov:
"KATRIN-2.5: Three-Dimensional Discrete-Ordinates Neutron, Photon and Charged
Particles Transport Code," User's guide, Report of Keldysh Inst. of Appl.
Math., Russian Ac. of Sci., No. 7-27-2004, Moscow (2004).
- A. M. Voloschenko, S. V. Gukov and A. V. Shwetsov:
"ARVES-2.5 - Preprocessor for the Working Macroscopic Cross-Section FMAC-M
Format for Transport Calculations," User's Guide, Report of Keldysh Inst. of
Appl. Math., Russian Ac. of Sci., No. 7-24-2004, Moscow (2004).
- A. M. Voloschenko:
"CEPXS-BFP: Version of Multigroup Coupled Electron-Photon Cross-Section
Generating Code CEPXS, Adapted for Solving the Charged Particle Transport in
the Boltzmann-Fokker-Planck Formulation with the Use of Discrete Ordinate
Method," User's Guide, Report of Keldysh Inst. of Appl. Math., Russian Ac. of
Sci., No. 7-36-2004, Moscow (2004).
- D. V. Gorbatkov, V. P. Kryuchkov, O. V. Sumaneev:
"SADCO-2.4: A Modular Code System for Generating Coupled Nuclear Data Libraries
to Provide High-Energy Particle Transport Calculation by Multigroup Methods,"
User's Guide, Institute for High-Energy Physics (2005).
- M. I. Gurevich, A. A. Russkov, A. M. Voloschenko:
"ConDat 1.0 - Code for Converting by the Tracing Algorithm the Combinatorial
Geometry Presentation to the Bit-Mapped One, Users Guide," Preprint of Keldysh
Inst. of Appl. Math., Russian Ac. of Sci., No. 12 (2007).
- M. I. Gurevich:
"Geometrical Module NCG," Part 2.8 of Report of RRC Kurchatov Institute No.
36/17-2006, Moscow (2006).
- D. A. Shkarovski:
"MCU Viewer," Part 14.3 of Report of RRC Kurchatov Institute No. 36/17-2006,
Moscow (2006).
- A. M. Voloschenko:
"SYNTH: Utility for Construction of an Approximate Solution of 3D Transport
Equation in Vicinity of Reactor Pressure Vessel by the Synthesis Method,"
User's Guide, Report of Keldysh Inst. Of Appl. Math., Russian Ac. of Sci., No.
7-36-2007, Moscow (2007).

11. HARDWARE REQUIREMENTS

All codes of the code system run on Intel Core 2 Duo and Core i7 PC equipped with 2.0-12.0 Gb RAM and 40-200 Gb HD memory under Windows XP/XP 64 Edition/Vista 64-bit. The use of SSD or RAID 0 SAS/SATA-2 HD arrays to decrease the run time of problem calculation, especially in solving 3D problems, is recommended.

Tested at the NEA Databank on:
- COMPUTER : Dell INTEL Duo E6550, 2.33 GHz (for Windows)
- OPERATING SYSTEM : DOS, under Windows XP Pro SP 3
- COMPILER: lahey/Fujitsu F 95 v7.1 (Windows), for few routines compiled

13. SOFTWARE REQUIREMENTS

The Fortran 90 language standard is followed closely. The Intel Visual Fortran 11.1 compiler is recommended to make the multi-threaded PC executables. The Compaq Visual Fortran 6.6C compiler can also be used to make the PC serial executables for solving problems, which require the RAM memory volume < 2 Gb. Some routines from IMSL library are used for estimation of spectral shape of acceleration corrections in outer iterations acceleration algorithm. Commercially available graphical software codes GRAPHER and SURFER are used to visualize geometry/results of calculations.

15. NAME AND ESTABLISHMENT OF AUTHORS

Contributed by: Radiation Shielding Information Computational Center
                Oak Ridge National Laboratory
                Oak Ridge, Tennessee, USA
Developed by:   Keldysh Institute of Applied Mathematics, Moscow, Russia

Fortran source
Makefiles to compile/link
Executables
Sample problem input/output
Electronic documentation