Diffusion synthetic acceleration for one-cell block inversion in slab geometry

Journal Article · Thu Jul 01 04:00:00 EDT 1999 · Transactions of the American Nuclear Society

OSTI ID:20005774

Kim, K S; Palmer, T S

Many techniques are being used to provide efficient numerical solutions to the transport equation, which include the diffusion synthetic acceleration (DSA), multigrid method, and parallel processing. In DSA, a diffusion equation is used to precondition the standard source iteration (SI) technique. SI on the first-order form of the transport equation typically involves sweeping the grid along directions of particle travel. One- and two-cell block inversion (CI) methods can be used as an alternative to SI and allow for the independent (and perhaps parallel) solution of scalar flux unknowns in each one- or two-cell block. Although one- and two-CI are parallel friendly, they are currently limited in their applicability. The iterative performance of one-CI in slab geometry degrades as the cells become optically thick: The spectral radius approaches unity. One-CI is not unconditionally stable for some multidimensional discretizations, such as the linear discontinuous (LD) finite element method. Two-CI is effective in one spatial dimension, with parallelization and multigrid, but not for x-y geometry because of the x-y coupling problem. The goal of this work is to construct a one-cell block inversion technique that will be unconditionally stable and convergent for multidimensional finite element discretization techniques. The authors describe the first step toward that goal, the derivation and analysis of an acceleration technique for one-CI applied to the slab geometry lumped LD (LLD) equations. The analysis results are compared with the results of numerical test problems.

• Research Organization: Oregon State Univ., Corvallis, OR (US)
• OSTI ID: 20005774
• Journal Information: Transactions of the American Nuclear Society, Journal Name: Transactions of the American Nuclear Society Vol. 81; ISSN 0003-018X; ISSN TANSAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
COMPARATIVE EVALUATIONS
CONVERGENCE
FINITE ELEMENT METHOD
MESH GENERATION
NUMERICAL SOLUTION
SLABS
TRANSPORT THEORY