Acceleration of within group iteration for pin-by-pin calculations

Tengfei Zhang*, E. E. Lewis, M. A. Smith, W. S. Yang, Yongping Wang, Hongchun Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In thermal reactor physics fine mesh neutron diffusion calculations in which homogenization is only at the pin cell level are of considerable interest. However, the slow convergence of iterations on fine-mesh spatial grids limits their applicability to practical problems. We present here an efficient way to accelerate the within-group iterations for pin-by-pin calculations based on a two-dimensional heterogeneous variational nodal method (VNM). Response matrix (RM) equations are formulated that incorporate multiple pins within each node. Within the nodes, finite elements in the x-y plane are employed to describe the piecewise constant heterogeneous geometry. On the nodal interfaces orthogonal polynomials are employed to approximate current distributions. The RM equations are solved using the Red-Black Gauss-Seidel (RBGS) iteration. Investigations on the coarse nodes acceleration (CNA) by combining homogenized pin cell nodes into larger heterogeneous nodes are performed. A series of meshing schemes are examined with a 2D small modular reactor core problem. With sufficient interface expansion order, CNA do not cause significant errors to either eigenvalues or fission rate distributions compared with fine mesh calculations. It is demonstrated that CNA accelerate the RBGS iteration significantly and achieves favorable accuracy-efficiency trade-off.

Original languageEnglish (US)
Pages (from-to)225-235
Number of pages11
JournalAnnals of Nuclear Energy
StatePublished - Feb 2018


  • Acceleration of within-group iteration
  • Coarse nodes acceleration
  • Heterogeneous variational nodal method

ASJC Scopus subject areas

  • Nuclear Energy and Engineering


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