4. METHODS
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.
- 'Frontline-style' 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 1.24:
1. SPECT simulation parallel performance improvements.
2. Improved Differencing schemes.
3. Continuous run and command line option to load flux moments from previous run results.
4. Input deck processing improvements.
(Refer to change.log in the package for more details).