Acceleration of within group iteration for pin-by-pin calculations. (February 2018)

• Record Type: Journal Article
• Authors: Zhang, Tengfei; Lewis, E.E.; Smith, M.A.; Yang, W.S.; Wang, Yongping; Wu, Hongchun
• Is Part Of: Annals of nuclear energy. Volume 112(2018)
• Page Start: 225
• Page End: 235
• Publication Date: 2018-02
• Subjects: Heterogeneous variational nodal method -- Coarse nodes acceleration -- Acceleration of within-group iteration; Nuclear energy -- Periodicals; Nuclear engineering -- Periodicals; 621.4805
• DOI: 10.1016/j.anucene.2017.10.006
• Languages: English
• ISSNs: 0306-4549

Abstract

Highlights: A way to accelerate within-group iterations for pin-by-pin calculations is proposed. The method is based on a two-dimensional heterogeneous variational nodal method. Heterogeneous nodes reduce the degrees of freedom of with-in group iterations. The accuracy is ensured by increasing interface polynomial orders. Abstract: 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.