A new and rigorous SP N theory for piecewise homogeneous regions

Chao, Y.

doi:10.1016/j.anucene.2016.06.010

Cited by 22 publications

(6 citation statements)

References 9 publications

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“…where the first and second parts on the right hand side contain only spherical harmonics of degree ( − 1) and ( + 1), respectively. This formula can be proved with solid spherical harmonics [94].…”

Section: Basicsmentioning

confidence: 90%

Rattlesnake Theory Manual

Wang

Labouré

2018

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Rattlesnake is built on the MOOSE framework. Rattlesnake manages meshes with libMesh [25] and solves the system equation with PETSc [26] through MOOSE. Support of unstructured meshes, parallelization with domain decomposition, various time integration schemes, most of nonlinear solvers features, multiphysics coupling are all inherited from the framework. Rattlesnake is responsible for setting up the discretization of RTE with interfaces provided by MOOSE. Because Rattlesnake is built on a general framework, it can perform calculations in 1D, 2D and 3D unstructured meshes via MPI (message passing interface) [27] and multi-threading. The weak forms can be directly translated into code under the MOOSE framework, which results in codes easy to maintain and extend. Multiple developers can co-work seamlessly on Rattlesnake. This development pattern allows splitting the work into the physics-related items residing in Rattlesnake, and physics-irrelevant items residing in the framework. The benefit is twofold: Rattlesnake can push the development on the framework side, which can benefit all the other MOOSE-based applications and any improvements in MOOSE can improve Rattlesnake. For example, the common software development procedure is managed by MOOSE, e.g. the version control, regression tests, on-line documentation. In addition, coupling Rattlesnake with other MOOSE-based applications dealing with other physics is straightforward because these applications are based on the same framework. As an example, the reactor physics application MAMMOTH [2, 28] leverages components spread over Rattlesnake, MOOSE and its modules, Bison [29, 30, 31], and Relap-7 [32]. In summary, being built on MOOSE makes Rattlesnake powerful and unique. There indeed are constraints imposed by the framework, but this is not insurmountable and outweighted by all the advantages provided by this development pattern. In Section 2, we first state the RTE for various particles. Currently, we only consider two particles: neutron and thermal radiation but Rattlesnake can be extended easily to other types. Particles mostly share the same time derivative,

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Section: Basicsmentioning

confidence: 90%

Rattlesnake Theory Manual

Wang

Labouré

2018

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“…Homogenization errors for pin computations are the main concern in these approximations, and they have been recently studied for different problems [12,13]. The main issue has been the definition of the discontinuity factors for the SP N approximation in two-or three-dimensional problems [14,15,16,17]. On the other hand, the SP N approximation has been implemented using the finite element method (FEM) for the spatial discretization [18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Pin-wise homogenization for SPN neutron transport approximation using the finite element method

Vidal-Ferràndiz¹,

González-Pintor²,

Ginestar³

et al. 2018

Journal of Computational and Applied Mathematics

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“…By generalizing the angular domain from S 2 (i.e., the unit sphere) to R 3 Ackroyd et al used properties of solid harmonics to introduce additional harmonics, perform Galerkin projection, restrict the relaxed equations back to S 2 , and thereby derive the SP N equations for steady-state, anisotropic scattering problems in homogeneous media [10,11]. Later, Hanuš used solid harmonics in tensor form and derived the SP 3 equations for steady-state isotropic-scattering problems [12]; Chao was also able to use the solid harmonics approach to show that Pomraning's angular flux trial space, which can lead to the SP N equations [13], is a particular solution to the steady-state isotropic-scattering transport equation [14].…”

Section: Introductionmentioning

confidence: 99%

Mathematical and Numerical Validation of the Simplified Spherical Harmonics Approach for Time-Dependent Anisotropic-Scattering Transport Problems in Homogeneous Media

McClarren

2017

Journal of Computational and Theoretical Transport

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In this work, we extend the solid harmonics derivation, which was used by Ackroyd et al to derive the steady-state SP N equations, to transient problems.The derivation expands the angular flux in ordinary surface harmonics but uses harmonic polynomials to generate additional surface spherical harmonic terms to be used in Galerkin projection. The derivation shows the equivalence between the SP N and the P N approximation. Also, we use the line source problem and McClarren's "box" problem to demonstrate such equivalence numerically. Both problems were initially proposed for isotropic scattering, but here we add higherorder scattering moments to them. Results show that the difference between the SP N and P N scalar flux solution is at the roundoff level.

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A new and rigorous SP N theory for piecewise homogeneous regions

Cited by 22 publications

References 9 publications

Rattlesnake Theory Manual

Rattlesnake Theory Manual

Pin-wise homogenization for SPN neutron transport approximation using the finite element method

Mathematical and Numerical Validation of the Simplified Spherical Harmonics Approach for Time-Dependent Anisotropic-Scattering Transport Problems in Homogeneous Media

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