**RSICC CODE
PACKAGE CCC-759**

** **

**1.
NAME AND TITLE**

TITAN 1.29: A Three-Dimensional Deterministic Radiation Transport Code System.

** **

**Main Code**:

TITAN 1.29s: serial version

TITAN 1.29p: parallel version

**Auxiliary Code:**

PENMSHXP 2.66b: Mesh Generator to Build TITAN or PENTRAN Input Deck with the DISLIN graphic library.

PENMSHXP 2.61a: Mesh Generator to Build TITAN or PENTRAN Input Deck without the DISLIN graphic library.

**2.
CONTRIBUTORS**

Georgia Institute of Technology.

**3.
CODING LANGUAGE AND COMPUTER**

Fortran 90/95/2003; PC/MAC, LINUX clusters (C00759PCX8604).

**4.
NATURE OF PROBLEM SOLVED**

TITAN is a time-independent deterministic radiation transport simulation code in 3-D Cartesian geometry. The hybrid approach in the TITAN code allows different transport solvers (Sn or Ray-tracing) to be applied in different regions. TITAN solves both the k-effective and fixed source forward/adjoint problems. It has been benchmarked on a number of OECD/NEA benchmark problems:

•3D Radiation Transport Benchmarks for Simple Geometries with Void Regions (Kobayashi problem)

•Benchmark on Deterministic Transport Calculations Without Spatial Homogenisation MOX Fuel Assembly 3-D Extension Case (C5G7 MOX)

•Benchmarking the Accuracy of Solution of 3-Dimensional Transport Codes and Methods over a Range in Parameter Space

(A summary report can be found at http://152.1.56.47/report/)

The extra sweep with fictitious quadrature technique enables TITAN to simulate the SPECT (Single Photon Emission Computed Tomography) projection images. SPECT simulations generally are performed by Monte Carlo codes. A benchmark using the TITAN code on a torso phantom has been established. In the TITAN SPECT simulation, collimators are not explicitly simulated, instead, a technique, called Circular Ordinate Splitting, is used to simulate the collimator blurring effects.

**5.
METHOD OF SOLUTION**

TITAN numerically solves the time-independent first order transport equation (Linear Boltzmann Equation) using a hybrid Discrete Ordinate (Sn) and Ray-tracing method. Two transport solvers, an Sn Solver and a ray-tracing solver, are integrated in the TITAN code. Both solvers work on the coarse mesh level in Cartesian geometry. Generally, a TITAN problem model contains more than one coarse mesh. This allows users to apply different solvers to different coarse mesh. This feature can be useful for problems containing a large region of low scattering medium. In such regions, the Sn method requires finer angular and spatial meshing and becomes less efficient. TITAN’s ray-tracing solver is more efficient to solve the transport equation in such regions. The ray-tracing solver is essentially a 3-D Method of Characteristics solver, only it applies to an individual coarse mesh, instead of the whole spatial domain. Currently the ray-solver applies only on coarse mesh with one material region, and the total cross-section of the material should be close to zero to qualify as ‘low scattering’ medium. For a multi-region regular coarse mesh, the Sn solver should be used.

TITAN uses the object oriented programming paradigm with a layered and modular structure. Some features of the code include:

• Integrated SN and ray-tracing solvers

• Shared scattering source kernel allowing arbitrary order anisotropic scattering

• Backward ray-tracing

• Block-oriented data structure allowing localized quadrature sets and solvers

• Layered code structure

• Level-symmetric and Pn-Tn quadrature sets

• Incorporation of three ordinate splitting techniques (rectangular, local PN-TN, and circular)

• Fast and memory-efficient spatial and angular projections on the interfaces of coarse meshes by using sparse projection matrix

• wave-front interface flux handling

• A binary I/O library to visualize and post-process data with TECPLOT

• Extra Sweep technique with the fictitious quadrature technique for calculations of angular fluxes along arbitrary directions

What’s new in Version 1.29:

1. Added the Lobatto-Chebyshev quadrature which includes a direction along an axis

2. Improved angular source handling

3. Improved parallel performance

(Refer to change.log in the package for more details)

**6.
RESTRICTIONS OR LIMITATIONS**

None noted.

**7.
TYPICAL RUNNING TIME**

Run times vary with processor speed and problem parameters.

**8.
COMPUTER HARDWARE REQUIREMENTS**

TITAN runs on personal computers and linux clusters.

**9.
COMPUTER SOFTWARE REQUIREMENTS**

Both TITAN and PENMSHXP are written in FORTRAN 90/95/2003 language. The FORTRAN 2003 features in the codes are limited to some user-defined data objects and some I/O statements. Most up-to-date FORTRAN compliers should be able to compile both codes. Portland FORTRAN compiler (ver. 8.0 or higher), Intel FORTRAN compilers (ver. 10.0 or higher), and GCC/GFORTRAN (ver. 4.3) are tested in WINDOWS/LINUX 32/64 bit systems. The codes also can be compiled on MAC OS X with Inter FORTRAN for MAC or GFORTRAN/GCC installed. For the parallel TITAN version, an MPI2 implementation is required, such as MPICH2, Microsoft MPI, Intel MPI, or OpenMPI on WINDOWS/LINUX. Further instructions on how to compile the codes are included in the package.

For PENMSHXP v2.64b, it is the user’s responsibility to ensure that access to DISLIN is in compliance with the makers of the DISLIN library (www.mps.mpg.de/dislin/). PENMSHXP also utilizes TECPLOT software if available for 3-D rendering with macro support http://www.tecplot.com/. A DISLIN-free version of PENMSHXP (ver. 2.61a) is also included. Ver 2.61a does not generate graphic output files. Instead, it generates a binary data file, which can be loaded with TECPLOT to render various plots.

**10.
REFERENCES**

**a.
included documentation:**

Ce Yi, “TITAN: A 3-D Deterministic Radiation Transport Code; User Manual Version 1.29,” Georgia Institute of Technology (2012).

Ce Yi and A. Haghighat, “PENMSHXP Manual, Version 2.66b,” Georgia Institute of Technology (2011).

**b. background information:**

Ce Yi and A. Haghighat, “A
Three-Dimensional Block-Oriented Hybrid Discrete Ordinates and Characteristics
Method,”* Nucl. Sci. Eng., ***164**:3, 221–247 (March 2010).

**11.
CONTENTS OF CODE PACKAGE**

The package is transmitted on one CD-rom in a ZIP file which contains the references cited above, PENMSHXP and TITAN source codes, executables, and sample problem input and output.

**12.
DATE OF ABSTRACT**

April 2011, July 2012.

**KEYWORDS:** DISCRETE
ORDINATES; RAY-TRACING; TRANSPORT