A Three-Dimensional Block-Oriented Hybrid Discrete Ordinates and Characteristics Method

In this paper, we present a hybrid formulation/algorithm to solve the linear Boltzmann equation, specifically for application to problems containing regions of low scattering. The hybrid approach uses the characteristics method in low scattering regions, while the remaining regions are treated with the discrete ordinates method (SN). A shared scattering kernel allows an arbitrary order of anisotropic scattering in both block-oriented solvers. A new three-dimensional transport code (TITAN) has been developed based on the hybrid approach. TITAN divides a problem model into coarse meshes (blocks) in the Cartesian geometry. The block-oriented structure allows different fine-meshing schemes (or characteristic ray densities) and angular quadrature sets for different coarse meshes. Angular and spatial projection techniques are developed to transfer angular fluxes on the interfaces of the coarse meshes. We have tested the performance and accuracy of the new hybrid algorithm within the TITAN code for a number of benchmark problems. The results of a computed tomography model and the Kobayashi benchmark problems are presented in this paper. It is demonstrated that while preserving high-level accuracy as compared to reference Monte Carlo simulations, the hybrid algorithm achieves significant computation efficiency as compared to the SN method only.