Discontinuity Factors for Simplified P3 Theory

Yamamoto, Akio; Sakamoto, Tatsuya; Endo, Takao

doi:10.13182/nse15-102

Cited by 11 publications

(3 citation statements)

References 15 publications

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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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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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“…We try to reduce the homogenization error using pin-wise homogenization. We use one dimensional geometries because the ambiguity in the definition of the flux discontinuity factors does not exist (Yu, Lu, and Chao, 2014;Yamamoto, Sakamoto, and Endo, 2016). As mentioned before, the one dimensional SP N approximation is equivalent to the complete P N approximation.…”

Section: Homogenization Strategy For Simplified Harmonic Equations (Smentioning

confidence: 99%

“…Homogenization errors for pin computations are the main concern in these approximations, and they have been recently studied for different problems (Kozlowski et al, 2011;Yu, Lu, and Chao, 2014). The main issue has been the definition of the discontinuity factors for the SP N approximation in two-or three-dimensional problems (Yu and Chao, 2015;Chao, 2016b;Chao, 2016a;Yamamoto, Sakamoto, and Endo, 2016). On the other hand, the SP N approximation has been implemented using the finite element method (FEM) for the spatial discretization (Turcksin, Ragusa, and Bangerth, 2010;Ragusa, 2010;Zhang, Ragusa, and Morel, 2013).…”

Section: Introductionmentioning

confidence: 99%

Development of a finite element method for neutron transport equation approximations

Ferràndiz¹

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Supervisors: Damián Ginestar Peiró Gumersindo Verdú Martín Ací em pariren i ací estic. I com que he investigat certes coses, ací les conte, ací les dic. AbstractThe neutron transport equation describes the neutron population and the nuclear reactions inside a nuclear reactor core. First, this equation is introduced and its assumptions are stated. Then, the stationary neutron diffusion equation which is the most useful approximation of this equation, is studied. This approximation leads to a differential eigenvalue problem. To solve the neutron diffusion equation, a h ≠ p finite element method is investigated. To improve the efficiency of the method a Restricted Additive Schwarz preconditioner is implemented.Once the solution for the steady state neutron distribution is obtained, it is used as initial condition for the time integration of the neutron diffusion equation. To test the behaviour of the method, rod ejection accidents are numerically simulated. However, a non-physical behaviour appears when a cell is partially rodded: this is, the rod cusping effect, which is solved by using a moving mesh scheme. In other words, the mesh follows the movement of the control rod. Numerical results show that the rod cusping effect is corrected with this scheme.After that, the simplified spherical harmonics approximation, SP N , is developed to solve the steady state problem. This approximation extends the spherical harmonics approximation, P N , in one dimensional geometries to multidimensional geometries with strong assumptions. It improves the diffusion theory results but does not converge as N tends to infinity. The advantages and limitations of this approximation are tested on several one-, two-and three-dimensional reactors.Finally, the spatial homogenization in the context of the finite element method is studied. Homogenization consists in replacing heterogeneous subdomains by homogeneous ones, in such a way that the homogenized problem provides fast and accurate average results. Discontinuous solutions were proposed in the Generalized Equivalence Theory. Here, a discontinuous Galerkin finite element method where the jump condition for the neutron flux is imposed in a weak sense using interior penalty terms is introduced. Also, the use of discontinuity factors for the correction of the homogenization error when using the SP N equations is investigated.v ResumenLa ecuación del transporte neutrónico describe la población de neutrones y las reacciones nucleares dentro de un reactor nuclear. Primero, introducimos esta ecuación y las aproximaciones de la misma. Entonces, estudiamos la ecuación de la difusión neutrónica, la aproximación al transporte más utilizada. Para el caso estacionario, esta aproximación da lugar a un problema diferencial de valores propios. Para resolver la ecuación de la difusión se ha desarrollado un método de elementos finitos h≠p. Para mejorar la eficiencia del método se ha implementado un precondicionador del tipo Restricted Additive Schwarz.Una vez hemos obtenido la distribución neutrónica en ...

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A Next Generation Method for Light Water Reactor core analysis by using Global/Local Iteration Method with SP3

Lin

Liu

2018

Annals of Nuclear Energy

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Discontinuity Factors for Simplified P3 Theory

Cited by 11 publications

References 15 publications

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

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

Development of a finite element method for neutron transport equation approximations

A Next Generation Method for Light Water Reactor core analysis by using Global/Local Iteration Method with SP3

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