Discontinuous finite-element transport solutions in the thick diffusion limit in Cartesian geometry

Conference · Mon Jan 07 04:00:00 EST 1991

OSTI ID:6027668

Adams, M L

We analyze the behavior of discontinuous finite-element methods (DFEMs) for problems that contain diffusive regions. We find that in slab geometry most of these methods perform quite well, but that the same is not true in XY or XYZ geometry. In these geometries, we find that there are two distinct sets of DFEMS. Methods in one set produce unphysical solutions in diffusive regions; the other leading-order solutions that satisfy discretizations of the correct diffusion equation. We show that two simple properties of the finite-element weight functions are sufficient to guarantee that a DFEM belongs to the latter set. We show, however, that even these DFEMs suffer from several defects: their leading-order solutions are in general discontinuous, they satisfy diffusion discretizations that can be ill-behaved, and they may not be accurate given boundary layers that are not resolved by the spatial mesh. We discuss the practical significance of these defects, and we show that liberal modification of some DFEMs can eliminate the defects. We present numerical results from simple test problems; these fully agree with our analysis. 15 refs., 6 figs., 1 tab.

• Research Organization: Lawrence Livermore National Lab., CA (USA)
• Sponsoring Organization: DOE/DP
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6027668
• Report Number(s): UCRL-JC-104787; CONF-910414--17; ON: DE91007620
• Country of Publication: United States
• Language: English

Related Subjects

654001* -- Radiation & Shielding Physics-- Radiation Physics
Shielding Calculations & Experiments
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
DIFFUSION
ELECTROMAGNETIC RADIATION
ENERGY TRANSFER
EQUATIONS
FINITE ELEMENT METHOD
HEAT TRANSFER
NUMERICAL SOLUTION
RADIATION TRANSPORT
RADIATIONS
SCATTERING
THERMAL RADIATION