The linear source approximation and particle conservation in the Method of Characteristics for isotropic and anisotropic sources

Ferrer, R.; Rhodes, Joel

doi:10.1016/j.anucene.2018.01.023

Cited by 17 publications

(10 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The general method was simplified in the case of the isotropic and anisotropic LSA by Ferrer [49]; this also introduced the LS-P0 method, in which the isotropic source is spatially linear, but the anisotropic source components are spatially uniform within each cell. This LSA was also shown to be consistent with particle conservation under certain constraints and to be compatible with CMFD acceleration [50].…”

Section: Overviewsupporting

confidence: 53%

MPACT Theory Manual (V.4.3)

Larsen

Collins²,

Kochunas

et al. 2022

View full text Add to dashboard Cite

This manual presents the theory underlying the three-dimensional (3D) whole-core, pin-resolved neutron transport calculation methodologies employed in the MPACT code. MPACT's primary goal is to provide accurate sub-pin power distributions in a computationally efficient manner. To accomplish this, MPACT offers several different transport method options. The 2D/1D method, in which 3D problems are decomposed into an axial stack of radial "slices," is currently the most commonly used. In this option, two-dimensional (2D) planar solutions are provided by the method of characteristics (MOC), and axial solutions are provided via one-dimensional (1D) approximate diffusion, or P 3 solutions. The radial and axial solutions are coupled by (i) axial and radial transverse leakages, and (ii) a global 3D coarse mesh finite difference (CMFD) solve, which provides both acceleration and stability to the solution iteration scheme.The subsequent chapters of this manual present a range of topics, including MOC, CMFD, axial nodal transport solvers, 2D/1D, self-shielding, depletion, thermal-hydraulics, and transient methods. Development of the underlying theory of the 2D/1D method is presented, diagrams are included to highlight important algorithmic flow, and important concepts are discussed as appropriate. This manual is intended to be selfsufficient, but references to published articles and other materials are included for further reading.MPACT is a relatively new code, with new capabilities and many computational methods that did not exist until recently. This manual is an even newer document, with chapters written by several different code contributors working under time constraints. For these reasons, the manual is not yet complete and finalized.

show abstract

Section: Overviewsupporting

confidence: 53%

MPACT Theory Manual (V.4.3)

Larsen

Collins²,

Kochunas

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Finally, not all linear source reconstructions capture correctly the asymptotic diffusion limit. In what follows, following Ferrer and Rhodes III [6,7], we first outline a general linear-reconstruction procedure for an arbitrary function that will yield a method able to capture the asymptotic diffusion limit. Later, we use this reconstruction for the emission source in the HO solver, and derive the corresponding moment tallies needed.…”

Section: Linear Source Approximation and Tallyingmentioning

confidence: 99%

“…( 24), effectively, we must be able to evaluate the source term Q LO (x p (t) , t) given LO quantities. A key consideration for the source evaluation is the need to capture the asymptotic diffusion limit (a critical numerical property [15,14,13]), for which a linear (or higher order) representation of the relevant quantities E and T is needed [5,6,7,25]. Here, we consider a linear source reconstruction.…”

Section: Linear Source Approximation and Tallyingmentioning

confidence: 99%

“…Introducing a linear reconstruction reduces the number of cells 2 necessary to obtain a good representation of the source. We use the method proposed by Ferrer and Rhodes III [6,7] for MOC to obtain the linear representation of tallies. Adams et al [2] showed that linear source representation on a triangular mesh, and bi-linear on orthogonal, rectangular meshes are required to obtain the thick diffusion limit.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A multi-dimensional, moment-accelerated deterministic particle method for time-dependent, multi-frequency thermal radiative transfer problems

Hammer

Park

Chacòn

2019

Journal of Computational Physics

View full text Add to dashboard Cite

Thermal Radiative Transfer (TRT) is the dominant energy transfer mechanism in high-energy density physics with applications in inertial confinement fusion and astrophysics. The stiff interactions between the material and radiation fields make TRT problems challenging to model. In this study, we propose a multi-dimensional extension of the deterministic particle (DP) method. The DP method combines aspects from both particle and deterministic methods. If the emission source is known a priori, and no physical scattering is present, the intensity of a particle can be integrated analytically. This introduces no statistical noise compared to Monte-Carlo methods, while maintaining the flexibility of particle methods. The method is closely related to the popular method of long characteristics. The combination of the DPmethod with a discretely-consistent, nonlinear, gray low-order system enables an efficient solution algorithm for multi-frequency TRT problems. We demonstrate with numerical examples that the use of a linear-source approximation based on spatial moments improves the behavior of our method in the thick diffusion limit significantly.

show abstract

“…In the MOC method, the centroids coordinates of a region can be calculated with a track-based method [11]. Fig.…”

Section: Track-based Centroid Calculationmentioning

confidence: 99%

Demonstration of a Linear Prolongation CMFD Method on Moc

Wang

et al. 2021

EPJ Web Conf.

View full text Add to dashboard Cite

Coarse Mesh Finite Difference (CMFD) method is a very effective method to accelerate the iterations for neutron transport calculation. But it can degrade and even fail when the optical thickness of the mesh becomes large. Therefore several methods, including partial current-based CMFD (pCMFD) and optimally diffusive CMFD (odCMFD), have been proposed to stabilize the conventional CMFD method. Recently, a category of “higherorder” prolongation CMFD (hpCMFD) methods was proposed to use both the local and neighboring coarse mesh fluxes to update the fine cell flux, which can solve the fine cell scalar flux discontinuity problem between the fine cells at the bounary of the coarse mesh. One of the hpCMFD methods, refered as lpCMFD, was proposed to use a linear prolongation to update the fine cell scalar fluxes. Method of Characteristics (MOC) is a very popular method to solve neutron transport equations. In this paper, lpCMFD is applied on the MOC code MPACT for a variety of fine meshes. A track-based centroids calculation method is introduced to find the centroids coordinates for random shapes of fine cells. And the numerical results of a 2D C5G7 problem are provided to demonstrate the stability and efficiency of lpCMFD method on MOC. It shows that lpCMFD can stabilize the CMFD iterations in MOC method effectively and lpCMFD method performs better than odCMFD on reducing the outer MOC iterations.

show abstract

The linear source approximation and particle conservation in the Method of Characteristics for isotropic and anisotropic sources

Cited by 17 publications

References 19 publications

MPACT Theory Manual (V.4.3)

MPACT Theory Manual (V.4.3)

A multi-dimensional, moment-accelerated deterministic particle method for time-dependent, multi-frequency thermal radiative transfer problems

Demonstration of a Linear Prolongation CMFD Method on Moc

Contact Info

Product

Resources

About