Blake W. Kelley

Stability and accuracy of 3D neutron transport simulations using the 2D/1D method in MPACT ☆

A consistent “2D/1D” neutron transport method is derived from the 3D Boltzmann transport equation, to calculate fuel-pin-resolved neutron fluxes for realistic full-core Pressurized Water Reactor (PWR) problems. The 2D/1D method employs the Method of Characteristics to discretize the radial variables and a lower order transport solution to discretize the axial variable. This paper describes the theory of the 2D/1D method and its implementation in the MPACT code, which has become the whole-core deterministic neutron transport solver for the Consortium for Advanced Simulations of Light Water Reactors (CASL) core simulator VERA-CS. Several applications have been performed on both leadership-class and industry-class computing clusters. Results are presented for whole-core solutions of the Watts Bar Nuclear Power Station Unit 1 and compared to both continuous-energy Monte Carlo results and plant data.

The Relationship Between the Coarse-Mesh Finite Difference and the Coarse-Mesh Diffusion Synthetic Acceleration Methods

Abstract The coarse-mesh finite difference (CMFD) and the coarse-mesh diffusion synthetic acceleration (CMDSA) methods are widely used, independently developed methods for accelerating the iterative convergence of deterministic neutron transport calculations. In this paper, we show that these methods have the following theoretical relationship: If the standard notion of diffusion synthetic acceleration as a fine-mesh method is straightforwardly generalized to a coarse-mesh method, then the linearized form of the CMFD method is algebraically equivalent to a CMDSA method. We also show theoretically (via Fourier analysis) and experimentally (via simulations) that for fixed-source problems, the CMDSA and CMFD methods have nearly identical convergence rates. Our numerical results confirm the close theoretically predicted relationship between these methods.