Accelerating the iterative convergence of high-fidelity discrete ordinates (SN) transport calculations is a central challenge in reactor safety analysis and licensing work. Standard methods each carry significant limitations. The Quasidiffusion (QD), also known as the Variable Eddington Factor (VEF), method converges rapidly but is inconsistent, with solutions differing from the SN solution by truncation errors. The Coarse Mesh Finite Difference (CMFD) and Diffusion Synthetic Acceleration (DSA) methods are consistent and converge rapidly for optically thin cells, but become unstable for optically thicker cells.
One thread of this project develops the Generalized Quasidiffusion (GQD) method, which achieves both consistency, producing the same converged solution as the unaccelerated SN equations, and unconditional stability for spatial cells of any optical thickness. This is accomplished through new consistent Eddington factors that enforce agreement between the high-order and low-order systems on any spatial grid.
A second thread addresses transport problems with highly forward-peaked scattering, a regime arising in many applications where standard angular discretization demands prohibitively fine quadrature. A modified Fokker-Planck acceleration technique, following a high-order/low-order (HOLO) scheme, preserves the angular flux and moments of the high-order transport equation, enabling efficient and accurate solutions without the angular resolution that standard methods require.
Doctoral Dissertations advised on the subject:
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Acceleration Of Particle Transport Iterations With ‘Consistent’ Eddington Factors
- Paganin, Tomas M. (2025)
- Ph.D. in Nuclear Engineering, The Ohio State University
- With E.W. Larsen as co-advisor
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A Fokker-Planck Acceleration Technique For Multiphysics Problems with Highly Forward-Peaked Scattering
- Kuczek, John J. (2021)
- Ph.D. in Nuclear Engineering, The Ohio State University