Meshless local Petrov–Galerkin solution of the neutron transport equation with streamline-upwind Petrov–Galerkin stabilization

•SUPG stabilization facilitates solution of the MLPG neutron transport equation.•MLS functions and SUPG stabilization permit enforcement of particle conservation.•Spatially-dependent cross sections are included directly in the weak form integration.•The MLPG equations exhibit second-order convergenc...

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Bibliographic Details
Published in:Journal of computational physics 2019-01, Vol.377, p.1-59
Main Authors: Bassett, Brody, Kiedrowski, Brian
Format: Article
Language:English
Subjects:
Approximation
Collocation methods
Computational physics
Computer simulation
Dependence
Eigenvalues
Finite element method
Galerkin method
Mathematical analysis
Meshless methods
MLPG
MLS
MMS
Monte Carlo simulation
Neutron flux
Neutron transport
Neutrons
Particle balance
SUPG
Transport equations
Weight
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Summary:•SUPG stabilization facilitates solution of the MLPG neutron transport equation.•MLS functions and SUPG stabilization permit enforcement of particle conservation.•Spatially-dependent cross sections are included directly in the weak form integration.•The MLPG equations exhibit second-order convergence to benchmark solutions. The meshless local Petrov–Galerkin (MLPG) method is applied to the steady-state and k-eigenvalue neutron transport equations, which are discretized in energy using the multigroup approximation and in angle using the discrete ordinates approximation. To prevent oscillations in the neutron flux, the MLPG transport equation is stabilized by the streamline upwind Petrov–Galerkin (SUPG) method. Global neutron conservation is enforced by using moving least squares basis and weight functions and appropriate SUPG parameters. The cross sections in the transport equation are approximated in accordance with global particle balance and without constraint on their spatial dependence or the location of the basis and weight functions. The equations for the strong-form meshless collocation approach are derived for comparison to the MLPG equations. The method of manufactured solutions is used to verify the resulting MLPG method in one, two and three dimensions. Results for realistic problems, including two-dimensional pincells, a reflected ellipsoid and a three-dimensional problem with voids, are verified by comparison to Monte Carlo simulations.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2018.10.028