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Title: A Least-Squares Transport Equation Compatible with Voids

Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transport equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S n formulation represents an excellent alternative to existing second-order S n transport formulations
 [1] ;  [1] ;  [1] ;  [1] ;  [2]
  1. Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering
  2. Idaho National Lab. (INL), Idaho Falls, ID (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 2332-4309; TRN: US1500077
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational and Theoretical Transport; Journal Volume: 43; Journal Issue: 1-7
Taylor and Francis
Research Org:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org:
Country of Publication:
United States
71 Classical and quantum mechanics, general physics; 97 Mathematical methods and computing; TRANSPORT THEORY; VOIDS; FINITE ELEMENT METHOD; LEAST SQUARE FIT; DIFFUSION; CONVERGENCE; SLABS; Iterative Methods; Limiting Values; One-Dimensional Calculations; second-order; Self-adjoint