STRATEGY FOR MULTIDIMENSIONAL NEUTRON GROUP DIFFUSION COMPUTATIONS

Technical Report · Wed Nov 01 04:00:00 EST 1961

OSTI ID:4760034

Wachspress, E L

In nuclear reactor design computations, one often solves the neutron group diffusion differential equations in two and three space dimensions. Finite difference techniques are used to reduce these differential equations to large systems of simultaneous linear equations. The basic statics problem is that of finding the fundamental neutron flux mode and its eigenvalue. Two distinct iterations are performed simultaneously, one on the fission neutron source (outer iteration) and the other on group fluxes (inner iteration) corresponding to a fixed fission source. Successive overrelaxation or alternating-directionimplicit iteration is used for the inner iteration. Chebyshev extrapolation or Wielandt's fractional iteration is used to accelerate convergence of the outer iteration. Theoretical optimization of-iteration parameters is possible for certain model problems, and such analysis guides strategy for more complex situations. Wielandt's method enhances outer iteration convergence at the expense of inner iteration convergence to give a net increase in computer time when successive over-relaxation is used for the inner iteration. On the other hand, Wielandt's method, together with alternating-direction-implicit inner iteration, can lead to a significant reduction in computation time. (auth)

• Research Organization: Knolls Atomic Power Lab., Schenectady, N.Y.
• DOE Contract Number: W-31-109-ENG-52
• NSA Number: NSA-17-007057
• OSTI ID: 4760034
• Report Number(s): TID-14262
• Country of Publication: United States
• Language: English

Related Subjects

EIGENVALUES
FINITE DIFFERENCE METHOD
MATHEMATICS
PHYSICS