Coarse-mesh diffusion synthetic acceleration in slab geometry

Journal Article · Sat Jul 01 04:00:00 EDT 2000 · Transactions of the American Nuclear Society

OSTI ID:20104470

Kim, K S; Palmer, T S

It has long been known that the success of a diffusion synthetic acceleration (DSA) scheme is very sensitive to the consistency between the discretization of the transport and diffusion acceleration equations. Acceleration schemes involving inconsistent discretizations have been successful, but no prescription is available that determines a priori an allowable degree of inconsistency. It is notable, however, that all current DSA schemes involve diffusion equations discretized on the spatial mesh used to solve the transport equations. Often the solution of a large number of low-order equations is an expensive part of the transport simulation. This motivates the desire to find stable and rapidly convergent acceleration schemes that are discretized on a mesh that is coarse relative to the transport mesh. The authors present here results showing that the low-order diffusion equation can be solved on a mesh coarser (by a factor of 2) than that used for the slab geometry transport equation. Their results show that coarse-mesh DSA is unconditionally stable and is as rapidly convergent as a DSA method discretized on the transport mesh. They have used Adams and Martin's modified four-step acceleration method (M4S) applied to the linear discontinuous (LD) finite element transport equations in slab geometry. To evaluate their procedure, they have performed a Fourier analysis to calculate theoretical spectral radii. They compare this analysis with convergence behavior observed in an implementation code for several model problems.

• Research Organization: Oregon State Univ., Corvallis, OR (US)
• OSTI ID: 20104470
• Journal Information: Transactions of the American Nuclear Society, Journal Name: Transactions of the American Nuclear Society Vol. 82; ISSN 0003-018X; ISSN TANSAO
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
CALCULATION METHODS
FOURIER ANALYSIS
MESH GENERATION
RADIATION TRANSPORT
SLABS