Advanced computational transport methods for curvilinear geometries. Final report

Technical Report · Wed Oct 30 04:00:00 EST 1991

OSTI ID:10137304

Martin, W R; Larsen, E W ^[1]; Palmer, T S; Adams, M L ^[2]

---

1. Michigan Univ., Ann Arbor, MI (United States). Dept. of Nuclear Engineering
2. Lawrence Livermore National Lab., CA (United States)

During the last year, a considerable effort was mounted to devise accurate and efficient numerical methods for the solution of curvilinear transport problems in the optically thick, diffusive regime. Much work has already been completed on these methods in slab and x-y geometries. The principle tool in designing these methods is an asymptotic analysis that permits one to theoretically assess the accuracy of a transport numerical method for diffusive regions in which the spatial grid is optically thick. A transport numerical method is said to be accurate for thick, diffusive problems if an asymptotic analysis yields an accurate discretized diffusion equation and accurate boundary conditions. If a given transport discretization has this property, then it is possible to incorporate this ``asymptotic`` diffusion equation into a diffusion synthetic acceleration (DSA) algorithm that will yield a very rapidly convergent iterative solution. The search for efficiently solvable DSA algorithms in one and two spatial dimensions has been going on for the past 20 years. Although many techniques are available now in one-dimensional geometries, in other geometries only the diamond differenced S{sub N} equations have been efficiently solved using conventional DSA. This is because this particular transport differencing yields a sufficiently simple low-order diffusion equation that lends itself to solution by multigrid methods. Conventional DSA when applied to most other transport discretizations leads to more complicated discrete diffusion equations that are not as efficiently solvable. The asymptotic analysis procedure outline here is an attempt to overcome this obstacle.

• Research Organization: Lawrence Livermore National Lab., CA (United States); Michigan Univ., Ann Arbor, MI (United States). Dept. of Nuclear Engineering
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 10137304
• Report Number(s): UCRL-CR--109223; ON: DE92011290
• Country of Publication: United States
• Language: English

Related Subjects

663620
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
99 GENERAL AND MISCELLANEOUS
990200
ALGORITHMS
ASYMPTOTIC SOLUTIONS
CURVILINEAR COORDINATES
MATHEMATICS AND COMPUTERS
PHYSICS OF RADIATIONS OTHER THAN NEUTRONS
PROGRESS REPORT
RADIATION TRANSPORT
TRANSPORT THEORY
TWO-DIMENSIONAL CALCULATIONS