A Decoupled Finite Element Heterogeneous Coarse Mesh Transport Method.
In a recent paper, an original finite element (FE) method was presented for solving eigenvalue transport problems on a coarse spatial mesh. The method employed a surface Green's function expansion of the angular flux trial functions, so that heterogeneous coarse-meshes could be treated with relative ease. Numerical problems were solved using the multigroup discrete ordinates approximation in one-dimensional (1-D) slab geometry. Unfortunately, difficulties were encountered in finding solutions to the algebraic finite element equations, which led to sizeable angular flux discontinuities at coarse-mesh interfaces and significant errors. For this reason, a nonvariational iterative technique was ultimately favored for converging the angular flux distribution, and was used in conjunction with a Rayleigh quotient for converging the eigenvalue. In this paper, a new derivation of finite element equations is presented, which seems to offer a remedy for at least some of the numerical ills that plagued the previous work. First, the equations are derived in terms of a generalized response function expansion. This allows a more efficient response basis to be employed and vastly reduces the overall computational effort without a substantial loss of accuracy. Second, the tight coupling between coarse-meshes in the original equations is effectively broken by assuming that an accurate estimate of the flux distribution entering a given coarse-mesh is known. With an additional assumption that an accurate eigenvalue estimate is known, an iterative approach to solving these decoupled finite element (DFE) equations is developed. The DFE method has been applied to both 1- and 2-D heterogeneous coarse-mesh problems with a far greater degree of success than the original FE method. However, some numerical difficulties remain to be overcome before the new approach can be considered robust.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 977950
- Report Number(s):
- LA-UR-05-0696; TRN: US201012%%589
- Resource Relation:
- Conference: Submitted to: American Nuclear Society Annual Summer Meeting, June 2005, San Diego, CA
- Country of Publication:
- United States
- Language:
- English
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