The Legendre Polynomial Axial Expansion Method

Abstract

This work presents a new formulation of the axial expansion transport method explicitly using Legendre polynomials for arbitrarily high-order expansions. This new formulation also features an alternative method of axial leakage calculation to allow for nonextruded flat source region meshes. This alternative axial leakage is introduced alongside a balance equation requirement to ensure that neutron balance is preserved in the coarse mesh for a given axial leakage formulation, which allows for effective coarse mesh finite difference acceleration. A matrix exponential table method is derived to allow for fast computations of arbitrarily high-order matrix exponentials for this work and precludes the need for further research into matrix exponential calculations for this method. Numerical results are presented that demonstrate the stability of the axial expansion method in systems with voidlike regions, showcase the speedup from matrix exponential tables, and investigate the axial convergence of the method in terms of both expansion order and mesh size.

Keywords:

• Method of characteristics
• MPACT
• 2D/1D
• matrix exponential tables

Acknowledgments

This material is based upon work supported under an Integrated University Program Graduate Fellowship. This research was supported by the Consortium for Advanced Simulation of Light Water Reactors (http://www.casl.govwww.casl.gov) and the Energy Innovation Hub for Modeling and Simulation of Nuclear Reactors (http://www.energy.gov/hubs) under U.S. Department of Energy contract number DE-AC05-00OR22725.

Disclosure Statement

No potential conflict of interest was reported by the author(s).