A three-dimensional variational nodal method for pin-resolved neutron transport analysis of pressurized water reactors

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

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


A three-dimensional variational nodal method (VNM) is presented for pressurized water reactor core calculations without fuel-moderator homogenization. The nodal functional is presented and discretized to obtain response matrix equations.Within the nodes, finite elements in the x-y plane and orthogonal polynomials in z are used to approximate the spatial flux distribution. On the lateral interfaces, orthogonal polynomials are employed. On the axial interfaces, the finite elements facilitate a spatially accurate current representation that has proven to be a challenge for the method of characteristics-based two-dimensional/one-dimensional approximations which typically rely on spatial homogenization. The angular discretization utilizes an evenparity integral method within the nodes, with the integrals evaluated using high-order Chebyshev-Legendre cubature. On the lateral and axial interfaces, low-order spherical harmonics (Pn) are augmented by high-order Pn expansions to which quasi-reflected conditions are applied. With quasi-reflected conditions, the solution converges to the high-order Pn solution for an infinite lattice of identical cells with no gradient, while the loworder Pn expansions handle global gradients in both the radial and axial directions. The method is implemented in the PANX code and applied first to a number of model problems to study convergence of the space-angle approximations and then to the C5G7 benchmark problems. Multigroup Monte Carlo solutions provide reference values for eigenvalues and pin-power distributions.

Original languageEnglish (US)
Pages (from-to)160-174
Number of pages15
JournalNuclear Science and Engineering
Issue number2
StatePublished - Nov 2017


  • Eliminating the fuel-moderator homogenization
  • Three-dimensional variational nodal method

ASJC Scopus subject areas

  • Nuclear Energy and Engineering


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