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Diffusion Acceleration Schemes for Self-Adjoint Angular Flux Formulation with a Void Treatment

Yaqi Wang, Hongbin Zhang, Richard C. Martineau

Nuclear Science and Engineering / Volume 176 / Number 2 / February 2014 / Pages 201-225

Technical Paper /

A Galerkin weak form for the monoenergetic neutron transport equation with a continuous finite element method and discrete ordinate method is developed based on self-adjoint angular flux formulation. This weak form is modified for treating void regions. A consistent diffusion scheme is developed with  projection. Correction terms of the diffusion scheme are derived to reproduce the transport scalar flux. A source iteration that decouples the solution of all directions with both linear and nonlinear diffusion accelerations is developed and demonstrated. One-dimensional Fourier analysis is conducted to demonstrate the stability of the linear and nonlinear diffusion accelerations. Numerical results of these schemes are presented.