Journal ArticleDOI
Discontinuous Finite Element Transport Solutions in Thick Diffusive Problems
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In this paper, the performance of discontinuous finite element methods (DFEMs) on problems that contain optically thick diffusive regions is analyzed and tested, and the asymptotic analysis is quite general.Abstract:
The performance of discontinuous finite element methods (DFEMs) on problems that contain optically thick diffusive regions is analyzed and tested. The asymptotic analysis is quite general; it holds...read more
Citations
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Journal ArticleDOI
Fast iterative methods for discrete-ordinates particle transport calculations
Marvin L. Adams,Edward W. Larsen +1 more
TL;DR: This Review discusses the theoretical foundations of the development of acceleration methods for iterative convergence of discrete-ordinates simulations, the important results that have been accomplished, and remaining open questions.
Journal ArticleDOI
Denovo: A New Three-Dimensional Parallel Discrete Ordinates Code in SCALE
TL;DR: Denovo is a new, three-dimensional, discrete ordinates (SN) transport code that uses state-of-the-art solution methods to obtain accurate solutions to the Boltzmann transport equation using nonstationary Krylov methods to solve the within-group equations.
Journal ArticleDOI
Krylov Iterative Methods and the Degraded Effectiveness of Diffusion Synthetic Acceleration for Multidimensional SN Calculations in Problems with Material Discontinuities
TL;DR: It is shown that as a preconditioner to the Krylov method, a partially consistent DSA method is more than adequate, and preferable to a fully consistent method because the partially consistent method is based on a continuous finite element discretization of the diffusion equation that can be solved relatively easily.
Book ChapterDOI
Advances in Discrete-Ordinates Methodology
Edward W. Larsen,Jim E. Morel +1 more
TL;DR: In this article, the authors review some of the major advances in discrete-ordinates (SN) calculations that have occurred since 1968, including faster speeds and larger memories of today's computers, enabling today's SN codes to simulate problems of much greater complexity, realism, and physical variety.
Journal ArticleDOI
Positive $P_N$ Closures
Cory D. Hauck,Ryan G. McClarren +1 more
TL;DR: A modification to the standard spherical harmonic closure used with linear kinetic equations of particle transport corrects this defect by requiring that the ansatz used to close the equations itself be a nonnegative function.
References
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Book
Computational Methods of Neutron Transport
Elmer E Lewis,W. F. Miller +1 more
TL;DR: In this paper, a balanced overview of the major methods currently available for obtaining numerical solutions in neutron and gamma ray transport is presented, focusing on methods particularly suited to the complex problems encountered in the analysis of reactors, fusion devices, radiation shielding, and other nuclear systems.
Journal ArticleDOI
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II
Edward W. Larsen,Jim E. Morel +1 more
TL;DR: In this article, a theoretical method is described for assessing the accuracy of transport differencing schemes in highly scattering media with optically thick spatial meshes and numerical results are presented that demonstrate the validity and accuracy of the analysis.
Journal ArticleDOI
A Linear-Discontinuous Spatial Differencing Scheme forSnRadiative Transfer Calculations
TL;DR: In this article, a 1D slab-geometry lumped linear-discontinuous scheme for the nonlinear radiative transfer equation and the associated material temperature equation is presented.
Journal ArticleDOI
The Asymptotic Diffusion Limit of Discretized Transport Problems
TL;DR: A well-known asymptotic analysis describes the transition of transport theory to diffusion theory in the limit of optically thick systems with small absorption and sources as discussed by the authors, and this analysis has been applied to a wide class of systems.
Journal ArticleDOI
Subcell balance methods for radiative transfer on arbitrary grids
TL;DR: In this paper, a new spatial discretization method was proposed to enforce conservation on quadrilateral subcells in an arbitrarily connected grid of polygonal cells, for two-dimensional radiative transfer problems.