Ce Yi

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

Abstract 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.

Benchmarking of PENTRAN-SSN Parallel Transport Code and FAST Preconditioning Algorithm Using the VENUS-2 MOX-Fueled Benchmark Problem

The discrete ordinates method (Sn) is the most widely used technique to obtain numerical solutions of the linear Boltzmann equation, and therefore to evaluate radiation fields and dose rates in nuclear devices. However, it is well known that this method suffers from slow convergence for problems characterized by optically thick media and scattering ratio close to unity. To address this issue we have developed a new preconditioning algorithm based on the even-parity simplified Sn (EP-SSN) equations. The new method is based on the flux acceleration simplified transport (FAST) algorithm which is implemented into the PENTRAN-SSN code system. The code system is designed for parallel computing architectures; PENTRAN-SSN features spatial, angular, and energy domain decomposition algorithms. The FAST preconditioner is parallelized with a spatial domain decomposition algorithm. In this paper, our objective is to test the performance of the new preconditioning system for a three-dimensional shielding calculation based on the VENUS-2 MOX-fueled benchmark problem, issued by OECD/NEA (Organization for Economic Co-operation and Development/Nuclear Energy Agency.

Validation of a new deterministic transport code for SPECT simulation

The simulation of single photon emission computed tomography (SPECT) has traditionally been done using Monte Carlo methods. However, the hybrid deterministic transport code TITAN is being benchmarked for the simulation of SPECT. The TITAN code is referred to as “hybrid” because it uses a discrete ordinates method in the phantom and a simplified ray-tracing algorithm in the air outside of the phantom. The TITAN code has been compared with the results of the SIMIND Monte Carlo code and experimental data of a myocardial perfusion phantom. In comparison with SIMIND, TITAN projection images were found to be in good visual agreement. However, maximum relative differences ranging from 13% to 26% were found when the projection images were compared numerically. These are believed to be the result of different cross-section information used in the codes and differences in how the codes represent collimation. A computation time comparison showed the advantage of the TITAN code over SIMIND when an increasing number of projection images are generated. The comparison with experimental data also resulted in excellent visual agreement with numerical differences of 21% to 30%, which are at least partially due to limitations of the experiment.