Unconditionally stable diffusion-acceleration of the transport equation

Journal Article · Thu Apr 01 04:00:00 EST 1982 · Transp. Theory Stat. Phys.; (United States)

DOI:https://doi.org/10.1080/00411458208230836· OSTI ID:6657490

Larson, E W

The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically thick regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems, the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results.

• Research Organization: University of California, Los Alamos National Laboratory, P. O. Box 1663, Los Alamos, New Mexico 87545
• OSTI ID: 6657490
• Journal Information: Transp. Theory Stat. Phys.; (United States), Journal Name: Transp. Theory Stat. Phys.; (United States) Vol. 11:1; ISSN TTSPB
• Country of Publication: United States
• Language: English

Related Subjects

654002 -- Radiation & Shielding Physics-- Shielding Calculations & Experiments-- (-1987)
654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
EIGENFUNCTIONS
EIGENVALUES
FUNCTIONS
NEUTRON TRANSPORT THEORY
NUMERICAL SOLUTION
SHIELDING
TRANSPORT THEORY