Bilinear nodal transport method in weighted diamond difference form
Nodal methods have been developed and implemented for the numerical solution of the discrete ordinates neutron transport equation. Numerical testing of these methods and comparison of their results to those obtained by conventional methods have established the high accuracy of nodal methods. Furthermore, it has been suggested that the linear-linear approximation is the most computationally efficient, practical nodal approximation. Indeed, this claim has been substantiated by comparing the accuracy in the solution, and the CPU time required to achieve convergence to that solution by several nodal approximations, as well as the diamond difference scheme. Two types of linear-linear nodal methods have been developed in the literature: analytic linear-linear (NLL) methods, in which the transverse-leakage terms are derived analytically, and approximate linear-linear (PLL) methods, in which these terms are approximated. In spite of their higher accuracy, NLL methods result in very complicated discrete-variable equations that exhibit a high degree of coupling, thus requiring special solution algorithms. On the other hand, the sacrificed accuracy in PLL methods is compensated for by the simple discrete-variable equations and diamond-difference-like solution algorithm. In this paper the authors outline the development of an NLL nodal method, the bilinear method, which can be written in a weighted diamond difference form with one spatial weight per dimension that is analytically derived rather than preassigned in an ad hoc fashion.
- Research Organization:
- Oak Ridge National Lab., TN
- OSTI ID:
- 5387969
- Report Number(s):
- CONF-870601-
- Journal Information:
- Trans. Am. Nucl. Soc.; (United States), Journal Name: Trans. Am. Nucl. Soc.; (United States) Vol. 54; ISSN TANSA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCURACY
ALGORITHMS
COMPUTERIZED SIMULATION
EFFICIENCY
FINITE DIFFERENCE METHOD
ITERATIVE METHODS
MATHEMATICAL LOGIC
NEUTRON TRANSPORT THEORY
NUMERICAL SOLUTION
SIMULATION
TRANSPORT THEORY
TWO-DIMENSIONAL CALCULATIONS