A Hybrid Deterministic/Monte Carlo Method for Solving the k-Eigenvalue Problem with a Comparison to Analog Monte Carlo Solutions

Abstract

In this article we present a hybrid deterministic/Monte Carlo algorithm for computing the dominant eigenvalue/eigenvector pair for the neutron transport k-eigenvalue problem in multiple space dimensions. We begin by deriving the Nonlinear Diffusion Acceleration method (Knoll, Park, and Newman, 2011; Park, Knoll, and Newman, 2012) for the k-eigenvalue problem. We demonstrate that we can adapt the algorithm to utilize a Monte Carlo simulation in place of a deterministic transport sweep. We then show that the new hybrid method can be used to solve a two-group, two dimensional eigenvalue problem. The hybrid method is competitive with analog Monte Carlo in terms of number of particle flights required to compute the eigenvalue; however it produces a much less noisy eigenvector and fission source distribution. Furthermore, we show that we can reduce the error induced by the discretization of the low-order system by appropriate refinement of the mesh.

Keywords:

• neutron transport
• k-eigenvalue problem
• hybrid methods
• moment-based acceleration

Additional information

Funding

This work was performed under U.S. government contract DE-AC52-06NA25396 for Los Alamos National Laboratory, which is operated by Los Alamos National Security, LLC, for the U.S. Department of Energy.

The work of C. T. Kelley has been partially supported by the Consortium for Advanced Simulation of Light Water Reactors (www.casl.gov), an Energy Innovation Hub (http://www,energy.gov/hubs) for Modeling and Simulation of Nuclear Reactors under U.S. Department of Energy Contract No. DE-AC05-00OR22725