Mesh-free method for numerical solution of the multi-group discrete ordinate neutron transport equation

Kashi, Samira; Minuchehr, A.; Zolfaghari, A.; Rokrok, B.

doi:10.1016/j.anucene.2017.03.034

Cited by 18 publications

(5 citation statements)

References 21 publications

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“…However, it can be seen that regarding the 4th eigenflux, the shape is similar. The following case corresponds to an homogeneous BWR cell [15,16]. The consideration of the upscattering in this case is one of the reasons why it was selected for this work.…”

Section: Mox Benchmark Problemmentioning

confidence: 99%

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Lambda modes comparison for different approximations of the neutron transport equation: Diffusion, SN and SP3

Morató

Kochunas

Miró

et al. 2021

Annals of Nuclear Energy

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Section: Mox Benchmark Problemmentioning

confidence: 99%

“…Case2: control rods half-inserted. A comparison of the multiplication factors, where the reference value was obtained with Monte Carlo method, is shown in table 16. FDM Diffusion result is also added in the comparison table.…”

Section: Fbr Takeda Benchmarkmentioning

confidence: 99%

Lambda modes comparison for different approximations of the neutron transport equation: Diffusion, SN and SP3

Morató

Kochunas

Miró

et al. 2021

Annals of Nuclear Energy

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“…The discrete ordinates radiation transport equation has been solved previously using meshless methods, including for collocation methods [11,12,13,14,15,16] and the meshless local Petrov-Galerkin (MLPG) method [17,18]. The collocation methods often use the second-order form of the radiation transport equation, such as the self-adjoint angular flux equation [19], while the MLPG methods use a background mesh for the integration.…”

Section: Introductionmentioning

confidence: 99%

Meshless discretization of the discrete-ordinates transport equation with integration based on Voronoi cells

Bassett¹,

Owen²

2020

Preprint

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The time-dependent radiation transport equation is discretized using the meshless-local Petrov-Galerkin method with reproducing kernels. The integration is performed using a Voronoi tessellation, which creates a partition of unity that only depends on the position and extent of the kernels. The resolution of the integration automatically follows the particles and requires no manual adjustment. The discretization includes streamlineupwind Petrov-Galerkin stabilization to prevent oscillations and improve numerical conditioning. The angular quadrature is selectively refineable to increase angular resolution in chosen directions. The time discretization is done using backward Euler. The transport solve for each direction and the solve for the scattering source are both done using Krylov iterative methods. Results indicate first-order convergence in time and second-order convergence in space for linear reproducing kernels.

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“…The chosen 2D cases are: first a MOX test problem found in [Capilla et al, 2008], the second one is a simple BWR cell test problem found in [Stepanek et al, 1982], [Kashi et al, 2017], the next one is the BWR rod bundle test also from [Kashi et al, 2017] and the last one is the common 2D C5G7 bechmark [Smith et al, 2003].…”

Section: Numerical Results For Criticality Problemsmentioning

confidence: 99%

“…The second case is a homogeneous BWR cell [Stepanek et al, 1982, Kashi et al, 2017. This case has been selected due to the fact that it is modeled with upscattering.…”

Section: Bwr Cell Test Problemmentioning

confidence: 99%

Contributions to solve the Multi-group Neutron Transport equation with different Angular Approaches

Rafet¹

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The most accurate way to know the movement of the neutrons through matter is achieved by solving the Neutron Transport Equation. Three different approaches to solve this equation have been investigated in this thesis: Discrete Ordinates Neutron Transport Equation, Neutron Diffusion Equation and Simplified Spherical Harmonics Equations.In order to solve the equations, different schemes of the Finite Differences Method were studied. The solution of these equations describes the population of neutrons and the occurred reactions inside a nuclear system. These variables are related with the flux and power, fundamental parameters for the Nuclear Safety Analysis.Por último, pero no menos importante, agradezco el apoyo de mi familia, mis hermanos y mi padre; y a los que me hacen sentir como tal, Jesús y Nati. Muy especialmente quiero dar las gracias a María, por estar siempre a mi lado e invitar a superarme. Finalmente, sería injusto no acordarme de mi madre a quien debo todo lo que soy.

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Mesh-free method for numerical solution of the multi-group discrete ordinate neutron transport equation

Cited by 18 publications

References 21 publications

Lambda modes comparison for different approximations of the neutron transport equation: Diffusion, SN and SP3

Lambda modes comparison for different approximations of the neutron transport equation: Diffusion, SN and SP3

Meshless discretization of the discrete-ordinates transport equation with integration based on Voronoi cells

Contributions to solve the Multi-group Neutron Transport equation with different Angular Approaches

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