Error Analysis of Variations on Larsen's Benchmark Problem
Error norms for three variants of Larsen's benchmark problem are evaluated using three numerical methods for solving the discrete ordinates approximation of the neutron transport equation in multidimensional Cartesian geometry. The three variants of Larsen's test problem are concerned with the incoming flux boundary conditions: unit incoming flux on the left and bottom edges (Larsen's configuration); unit, incoming flux only on the left edge; unit incoming flux only on the bottom edge. The three methods considered are the Diamond Difference (DD) method, and the constant-approximation versions of the Arbitrarily High Order Transport method of the Nodal type (AHOT-N), and of the Characteristic (AHOT-C) type. The cell-wise error is computed as the difference between the cell-averaged flux computed by each method and the exact value, then the L{sub 1}, L{sub 2}, and L{sub {infinity}} error norms are calculated. The results of this study demonstrate that while integral error norms, i.e. L{sub 1}, L{sub 2}, converge to zero with mesh refinement, the pointwise L{sub {infinity}} norm does not due to solution discontinuity across the singular characteristic. Little difference is observed between the error norm behavior of the three methods considered in spite of the fact that AHOT-C is locally exact, suggesting that numerical diffusion across the singular characteristic as the major source of error on the global scale. However, AHOT-C possesses a given accuracy in a larger fraction of computational cells than DD.
- Research Organization:
- Oak Ridge National Laboratory (US)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- AC05-00OR22725
- OSTI ID:
- 786337
- Report Number(s):
- P01-110943; TRN: US0108874
- Resource Relation:
- Conference: International Meeting on Mathematical Methods for Nuclear Applications, Salt Lake City, UT (US), 09/09/2001--09/13/2001; Other Information: PBD: 27 Jun 2001
- Country of Publication:
- United States
- Language:
- English
Similar Records
Behavior of the Diamond Difference and Low-Order Nodal Numerical Transport Methods in the Thick Diffusion Limit for Slab Geometry
A posteriori error estimators for the discrete ordinates approximation of the one-speed neutron transport equation
Related Subjects
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
BENCHMARKS
BOUNDARY CONDITIONS
DISCRETE ORDINATE METHOD
NEUTRON TRANSPORT
DATA COVARIANCES
NEUTRON TRANSPORT THEORY
DISCRETE ORDINATES TRANSPORT
DIAMOND DIFFERENCE METHOD
NODAL METHODS
CHARACTERISTICS METHODS
ERROR ANALYSIS