An augmented source method for the application of nodal equivalence theory
- Purdue Univ., West Lafayette, IN (United States). School of Nuclear Engineering
The application of nodal equivalence theory (NET) in multigroup diffusion theory has required the use of ``discontinuity factors`` (DFs) to account for the homogenization errors that are inherent in all coarse-mesh nodal methods. Traditionally, DFs have been applied directly to the nodal matrix equations as multipliers to the group constants. For most problems of practical interest, the application of DFs has not led to the divergence of the iterative methods used to solve the discretized nodal equations. However, because of the large discontinuity factors resulting from the steep flux gradients in the modular high-temperature gas reactor, the inner and upscatter iterations failed to converge, motivating an investigation into alternative methods for applying NET. In this work, the augmented source method (ASM) for applying NET to the nodal expansion method is introduced. External surface sources at a node boundary are introduced to account for the homogenization errors thereby preserving the original matrix properties for which convergence of iterative methods is guaranteed. The ASM produced converged solutions for any magnitude of DFs and reproduced the reference solution when the augmented sources were constructed from the reference quantities. The application of the ASM to the core depletion calculation demonstrated the use of various approximations for the augmented source. An augmented source, which was constant during the burnup cycle, resulted in an improved solution in which the eigenvalue error was reduced by a factor of 6 compared with the nodal solution without DFs.
- OSTI ID:
- 163180
- Journal Information:
- Nuclear Science and Engineering, Vol. 121, Issue 3; Other Information: PBD: Nov 1995
- Country of Publication:
- United States
- Language:
- English
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