Novel Approaches to Adaptive Angular Approximations in Computational Transport
The particle-transport equation is notoriously difficult to discretize accurately, largely because the solution can be discontinuous in every variable. At any given spatial position and energy E, for example, the transport solution can be discontinuous at an arbitrary number of arbitrary locations in the direction domain. Even if the solution is continuous it is often devoid of smoothness. This makes the direction variable extremely difficult to discretize accurately. We have attacked this problem with adaptive discretizations in the angle variables, using two distinctly different approaches. The first approach used wavelet function expansions directly and exploited their ability to capture sharp local variations. The second used discrete ordinates with a spatially varying quadrature set that adapts to the local solution. The first approach is very different from that in today’s transport codes, while the second could conceivably be implemented in such codes. Both approaches succeed in reducing angular discretization error to any desired level. The work described and results presented in this report add significantly to the understanding of angular discretization in transport problems and demonstrate that it is possible to solve this important long-standing problem in deterministic transport. Our results show that our adaptive discrete-ordinates (ADO) approach successfully: 1) Reduces angular discretization error to user-selected “tolerance” levels in a variety of difficult test problems; 2) Achieves a given error with significantly fewer unknowns than non-adaptive discrete ordinates methods; 3) Can be implemented within standard discrete-ordinates solution techniques, and thus could generate a significant impact on the field in a relatively short time. Our results show that our adaptive wavelet approach: 1) Successfully reduces the angular discretization error to arbitrarily small levels in a variety of difficult test problems, even when using the simplest wavelet basis (Haar); 2) Achieves a given error with fewer unknowns than non-adaptive discrete-ordinates or wavelet approaches; 3) Does not yet have an efficient enough solution technique to compete with discrete ordinates methods; 4) Shows enough promise that further research into solution techniques should be pursued.
- Research Organization:
- Texas A & M Univ., College Station, TX (United States). Texas A & M Engineering Experiment Station
- Sponsoring Organization:
- USDOE - Office of Nuclear Energy, Science and Technology (NE)
- DOE Contract Number:
- FG07-01ID14112
- OSTI ID:
- 883002
- Report Number(s):
- DOE-ID14112-final
- Country of Publication:
- United States
- Language:
- English
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