Particle Transport Acceleration with ‘Consistent’ Eddington Factors


We have developed a new Generalized Quasidiffusion (GQD) method to accelerate the iterative convergence of SN particle transport problems. The standard Quasidiffusion (QD) or Variable Eddington Factor (VEF) method converges rapidly but is inconsistent – its solution differs by truncation errors from the SN solution. The widely-used Coarse Mesh Finite Difference (CMFD) and Diffusion Synthetic Acceleration (DSA) methods are consistent and converge rapidly for optically thin spatial cells, but typically become unstable for optically thicker cells. The new GQD method possesses the positive features of these existing methods, but avoids their shortcomings. Like CMFD and DSA, the GQD method is consistent – it produces the same converged solution as the unaccelerated SN equations. And, like QD, the GQD method is unconditionally stable for problems with spatial cells of any optical thickness. The standard QD method employs Eddington factors that render the QD solution consistent only when the optical thickness of the spatial cells limits to 0. The GQD method employs new “consistent” Eddington factors that make the GQD solution consistent for any spatial grid. 

Publications


Particle transport acceleration with `consistent' Eddington factors


Tomas M. Paganin, Richard Vasques, Edward W. Larsen

Submitted to ANS M&C 2025


[J25] A 'consistent' quasidiffusion method for solving particle transport problems


Edward W. Larsen, Tomas M. Paganin, Richard Vasques

Nuclear Science and Engineering, 2024


[P39] A “consistent” quasidiffusion method for iteratively solving particle transport problems


Edward W. Larsen, Tomas M. Paganin, Richard Vasques

Proceedings of International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Niagara Falls, Canada, 2023 Aug


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