The Legendre Polynomial Axial Expansion Method

Journal Article · 05 July 2022 · Nuclear Science and Engineering

DOI: https://doi.org/10.1080/00295639.2022.2082231 · OSTI ID:1878679

Herring, Nicholas F.  ^[1]; Collins, Benjamin S.  ^[2]; Downar, Thomas J.  ^[1]; Graham, Aaron M.  ^[3]

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1. Univ. of Michigan, Ann Arbor, MI (United States)
2. Univ. of Texas, Austin, TX (United States)
3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

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. Here. 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.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1878679
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 2 Vol. 197; ISSN 0029-5639
• Publisher: Taylor & FrancisCopyright Statement
• Country of Publication: United States
• Language: English