Goal based mesh adaptivity for fixed source radiation transport calculations

Baker, C.M.J.; Buchan, Andrew G.; Pain, Christopher C.; Tollit, Brendan; Goffin, Mark A.; Merton, S.R.; Warner, P. C.

doi:10.1016/j.anucene.2012.11.029

Cited by 15 publications

(13 citation statements)

References 26 publications

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“…The symmetry of the Jacobian also makes possible the use of efficient symmetric solvers for Eq. (14).…”

Section: Riemann Procedures In Non-orthogonal Basesmentioning

confidence: 95%

“…Then, Eq. (14) simplifies to the standard eigenvalue problem (9) and the usual Riemann upwinding can be carried out. In non-orthogonal cases, however, the generalized eigenproblem has to be solved.…”

Section: Riemann Procedures In Non-orthogonal Basesmentioning

confidence: 99%

“…These studies have shown spatially adaptive refinement to give an important contribution to reducing the computational burden for Boltzmann problems. The reader is referred to [8,9,[13][14][15][16][17] for further details on current research in this area.…”

Section: Introductionmentioning

confidence: 99%

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A space–angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

Kópházi

Lathouwers

2015

Journal of Computational Physics

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“…The symmetry of the Jacobian also makes possible the use of efficient symmetric solvers for Eq. (14).…”

Section: Riemann Procedures In Non-orthogonal Basesmentioning

confidence: 95%

Section: Riemann Procedures In Non-orthogonal Basesmentioning

confidence: 99%

See 1 more Smart Citation

A space–angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

Kópházi

Lathouwers

2015

Journal of Computational Physics

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“…Adaptivity is one of main advantages in the use of the finite element method. h-adaptable meshes have been proposed to obtain the static configuration of a nuclear reactor core with the use of triangular finite elements [79] and rectangular elements [8]. Also unstructured grid schemes have been developed to solve the problem in non standard geometries [80].…”

Section: Hexagonal Reactors : Static Calculationmentioning

confidence: 99%

Approximation of The Neutron Diffusion Equation on Hexagonal Geometries Using a h-p finite element method

Moawad¹

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“…Adaptivity is one of the main advantages in the use of the finite element method. h-adaptable meshes have been proposed to be used to obtain the static configuration of a nuclear reactor core with the use of triangular finite elements (Baker et al, 2013) and rectangular elements (Wang, Bangerth, and Ragusa, 2009). Also unstructured grid schemes (Theler, 2013) have been developed to solve the problem in non standard geometries.…”

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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Goal based mesh adaptivity for fixed source radiation transport calculations

Cited by 15 publications

References 26 publications

A space–angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

A space–angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

Approximation of The Neutron Diffusion Equation on Hexagonal Geometries Using a h-p finite element method

Development of a finite element method for neutron transport equation approximations

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