Analysis of inherent oscillations in multidimensional S{sub N} solutions of the neutron transport equation

Journal Article · Sun Sep 01 04:00:00 EDT 1996 · Nuclear Science and Engineering

OSTI ID:379803

Petrovic, B G; Haghighat, A ^[1]

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1. Pennsylvania State Univ., University Park, PA (United States). Nuclear Engineering Dept.

Recent pressure vessel fast fluence calculations have revealed numerical difficulties (spatial oscillations) in the S{sub N} solutions, which have persisted in spite of mesh refinement. It is demonstrated that other shielding/deep-penetration applications may be affected; in fact, any S{sub N} solution in which the uncollided flux component is significant is likely to exhibit such difficulties. Test problems have been designed to characterize and understand numerical difficulties. Main analyses are performed using the diamond-difference (DD) scheme, which is linear and forms the basis for other (more complex) low-order differencing schemes. Other low-order differencing schemes (e.g., the DD with negative flux fixup and the {theta}-weighted) may partly remedy the situation by reducing the oscillations or by eliminating the oscillations at a cost of oversmoothing the results everywhere (e.g., the zero-weighted scheme). These schemes provide more robust solutions, but the inherent difficulties (although reduced) still remain. Types of discontinuities that trigger the oscillations are also examined; it is difficult to envisage an actual practical application free of such discontinuities. The magnitude of numerical difficulties (oscillations) and their practical relevance will depend on all S{sub N} model features, the differencing scheme being used, and the application requirements, but this study has shown that they are inherent to multidimensional finite-difference S{sub N} algorithms.

• OSTI ID: 379803
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 1 Vol. 124; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGORITHMS
DISCRETE ORDINATE METHOD
FINITE DIFFERENCE METHOD
MESH GENERATION
NEUTRON FLUX
NEUTRON TRANSPORT THEORY