Nonlinear Weighted Flux Methods for Particle Transport Problems in Two-Dimensional Cartesian Geometry

Roberts, Loren; Anistratov, Dmitriy Y.

doi:10.13182/nse08-48

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…Similar methodologies with this kind of domain decomposition can be developed on the basis of low-order equations of other methods, for example, the nonlinear diffusion acceleration [17] and nonlinear weighted flux methods [18]. The developed methods can be directly used for multigroup transport problems.…”

Section: Discussionmentioning

confidence: 99%

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Computational transport methodology based on decomposition of a problem domain into transport and diffusive subdomains

Anistratov

Stehle

2012

Journal of Computational Physics

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Section: Discussionmentioning

confidence: 99%

“…(17) and (18) to compute / n (n = 0,1). On every transport iteration, the angular flux w is used to compute the QD (Eddington) factor E (19) that provides an exact closure and serves as a coefficient of the LOQD equations.…”

Section: Computational Methodology With Domain Decomposition Based Onmentioning

confidence: 99%

Computational transport methodology based on decomposition of a problem domain into transport and diffusive subdomains

Anistratov

Stehle

2012

Journal of Computational Physics

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“…The low-order moment equations are closed with the high-order RT equation by means of prolongation operators and exact closures. The iteration methods for solving RT equation based on the NPA are the quasidiffusion (QD) method (aka Eddington Variable Factor (VEF) method), nonlinear diffusion acceleration, coarse-mesh finite differencing (CMFD) method, partial currentbased CMFD, α-weighted methods [13,15,16,17,18,19,20]. The NPA has been applied to TRT and radiation hydrodynamics problems [21,22,23,24,25,26,27,28,29].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Iterative Projection Methods with Multigrid in Photon Frequency for Thermal Radiative Transfer

Anistratov

2020

Preprint

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This paper presents nonlinear iterative methods for the fundamental thermal radiative transfer (TRT) model defined by the time-dependent multifrequency radiative transfer (RT) equation and the material energy balance (MEB) equation. The iterative methods are based on the nonlinear projection approach and use multiple grids in photon frequency. They are formulated by the highorder RT equation on a given grid in photon frequency and low-order moment equations on a hierarchy of frequency grids. The material temperature is evaluated in the subspace of the lowest dimensionality from the MEB equation coupled to the effective grey low-order equations. The algorithms apply various multigrid cycles to visit frequency grids. Numerical results are presented to demonstrate convergence of the multigrid iterative algorithms in TRT problems with large number of photon frequency groups.

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A hybrid transport-diffusion method for 2D transport problems with diffusive subdomains

Stehle

Anistratov

Adams

2014

Journal of Computational Physics

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Nonlinear Weighted Flux Methods for Particle Transport Problems in Two-Dimensional Cartesian Geometry

Cited by 4 publications

References 19 publications

Computational transport methodology based on decomposition of a problem domain into transport and diffusive subdomains

Computational transport methodology based on decomposition of a problem domain into transport and diffusive subdomains

Nonlinear Iterative Projection Methods with Multigrid in Photon Frequency for Thermal Radiative Transfer

A hybrid transport-diffusion method for 2D transport problems with diffusive subdomains

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