A Least-Squares Transport Equation Compatible with Voids

Journal Article · Mon Dec 01 00:00:00 EST 2014 · Journal of Computational and Theoretical Transport

DOI:https://doi.org/10.1080/00411450.2014.927364· OSTI ID:1177636

Hansen, Jon ^[1]; Peterson, Jacob ^[1]; Morel, Jim ^[1]; Ragusa, Jean ^[1]; Wang, Yaqi ^[2]

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1. Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering
2. Idaho National Lab. (INL), Idaho Falls, ID (United States)

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

• Research Organization: Idaho National Lab. (INL), Idaho Falls, ID (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC07-05ID14517
• OSTI ID: 1177636
• Report Number(s): INL/JOU-15-34854; TRN: US1500077
• Journal Information: Journal of Computational and Theoretical Transport, Vol. 43, Issue 1-7; ISSN 2332-4309
• Publisher: Taylor and Francis
• Country of Publication: United States
• Language: English

Related Subjects

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