US Air Force Institute of Technology, Wright-Patterson Air Force
Base, Ohio, 2007, AFIT DS ENP 07-S01, 146 pp.
The distribution iteration algorithm, developed by Wager and Prins, for solving the Boltzmann Transport Equation (BTE) has proven, with further development, to be a robust alteative to von Neumann iteration on the scattering source, aka source iteration (SI). Previous work with was based on the time-independent form of the transport equation. In this research, the algorithm was Improved to provide faster, more efficient, robust convergence: Extended to XYZ geometry, Extended to Multigroup Energy treatment, Extended to solve the time-dependent form of the Boltzmann Transport Equation.
The discrete ordinates equations for approximating the BTE have been solved using SI since the discrete ordinates method was developed at Los Alamos Scientific Laboratory by 1953. However, SI is often inefficient by itself and requires an accelerator in order to produce results efficiently and reliably. The acceleration schemes that are in use in production codes are Diffusion Synthetic Acceleration (DSA) and Transport Synthetic Acceleration (TSA). DSA is ineffective for some problems, and cannot be extended to high-performance spatial quadratures. TSA is less effective than DSA and fails for some problems. Krylov acceleration has been explored in recent years, but has many parameters that require problem-dependent tuning for efficiency and effectiveness.
The DI algorithm is an alteative to source iteration that, in our testing, does not require an accelerator. I developed a formal verification plan and executed it to verify the results produced by my code that implemented DI with the above features. A new, matrix albedo, boundary condition treatment was developed and implemented.
The distribution iteration algorithm, developed by Wager and Prins, for solving the Boltzmann Transport Equation (BTE) has proven, with further development, to be a robust alteative to von Neumann iteration on the scattering source, aka source iteration (SI). Previous work with was based on the time-independent form of the transport equation. In this research, the algorithm was Improved to provide faster, more efficient, robust convergence: Extended to XYZ geometry, Extended to Multigroup Energy treatment, Extended to solve the time-dependent form of the Boltzmann Transport Equation.
The discrete ordinates equations for approximating the BTE have been solved using SI since the discrete ordinates method was developed at Los Alamos Scientific Laboratory by 1953. However, SI is often inefficient by itself and requires an accelerator in order to produce results efficiently and reliably. The acceleration schemes that are in use in production codes are Diffusion Synthetic Acceleration (DSA) and Transport Synthetic Acceleration (TSA). DSA is ineffective for some problems, and cannot be extended to high-performance spatial quadratures. TSA is less effective than DSA and fails for some problems. Krylov acceleration has been explored in recent years, but has many parameters that require problem-dependent tuning for efficiency and effectiveness.
The DI algorithm is an alteative to source iteration that, in our testing, does not require an accelerator. I developed a formal verification plan and executed it to verify the results produced by my code that implemented DI with the above features. A new, matrix albedo, boundary condition treatment was developed and implemented.