Composite finite element solutions for neutron transport

Ackroyd, R.T.; Wilson, W.B.

doi:10.1016/0306-4549(88)90037-0

Cited by 9 publications

(6 citation statements)

References 14 publications

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“…We do not discuss other adapted angular discretisations, please see [4,8] for a detailed overview. [19,20] first used different P n expansion orders across space in a 1D test problem, where the expansion order was determined a priori. [21,22] then used the even-parity form of the BTE (which is well suited to P n simulations as neither work in voids) and built a matrix-free combined space/angle adaptive algorithm that used goal-based metrics and showed reductions in total NDOFs applied.…”

Section: Adaptivity With P Nmentioning

confidence: 99%

Angular adaptivity with spherical harmonics for Boltzmann transport

Dargaville

Buchan

Smedley-Stevenson

et al. 2019

Journal of Computational Physics

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This paper describes an angular adaptivity algorithm for Boltzmann transport applications which uses P n and filtered P n expansions, allowing for different expansion orders across space/energy. Our spatial discretisation is specifically designed to use less memory than competing DG schemes and also gives us direct access to the amount of stabilisation applied at each node. For filtered P n expansions, we then use our adaptive process in combination with this net amount of stabilisation to compute a spatially dependent filter strength that does not depend on a priori spatial information. This applies heavy filtering only where discontinuities are present, allowing the filtered Pn expansion to retain highorder convergence where possible. Regular and goal-based error metrics are shown and both the adapted P n and adapted filtered P n methods show significant reductions in DOFs and runtime. The adapted filtered P n with our spatially dependent filter shows close to fixed iteration counts and up to high-order is even competitive with P 0 discretisations in problems with heavy advection.

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Section: Adaptivity With P Nmentioning

confidence: 99%

Angular adaptivity with spherical harmonics for Boltzmann transport

Dargaville

Buchan

Smedley-Stevenson

et al. 2019

Journal of Computational Physics

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“…However, the group-dependent angular resolution does provide a smaller error for a given number of degrees of freedom. The group-dependent resolution provides an increase in performance because the thermal group (2) requires less resolution compared to the fast group (1). Examples of adapted angular resolutions are shown in figure 25.…”

Section: Regular Adaptivitymentioning

confidence: 99%

“…The literature shows that research has been undertaken in optimising each of these methods. The first known attempt to improve the efficiency of a transport calculation through adjusting the angular discretisation was by Ackroyd and Wilson [1]. In this work they use the even-parity (second-order) P N method in 1D with variable resolution over the spatial domain.…”

Section: Introductionmentioning

confidence: 99%

Goal-based angular adaptivity applied to the spherical harmonics discretisation of the neutral particle transport equation

Goffin¹,

Buchan²,

Belme³

et al. 2014

Annals of Nuclear Energy

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A variable order spherical harmonics scheme has been described and employed for the solution of the neutral particle transport equation. The scheme is specifically described with application within the inner-element sub-grid scale finite element spatial discretisation. The angular resolution is variable across both the spatial and energy dimensions. That is, the order of the spherical harmonic expansion may differ at each node of the mesh for each energy group. The variable order scheme has been used to develop adaptive methods for the angular resolution of the particle transport phase-space. Two types of adaptive method have been developed and applied to examples. The first is regular adaptivity, in which the error in the solution over the entire domain is minimised. The second is goal-based adaptivity, in which the error in a specified functional is minimised. The methods were applied to fixed source and eigenvalue examples. Both methods demonstrate an improved accuracy for a given number of degrees of freedom in the angular discretisation.

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“…In this section, we evaluate the behaviour of our solver in controlled settings using several classic testing cases which serve as benchmarks for other similar codes that use deterministic methods to obtain the solution. We have selected the tests of Reed [16,22], Alcouffe [16], a deep penetration analysis with two energy groups [23] and one case of anisotropic scattering with three energy groups in a series of consecutive materials [24,25].…”

Section: Classic Literature Testsmentioning

confidence: 99%

Validating NEUTRO, a deterministic finite element neutron transport solver for fusion applications, with literature tests, experimental benchmarks and other neutronic codes

Goldberg¹,

Duxans²,

Gelabert³

et al. 2022

Plasma Phys. Control. Fusion

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Neutron reactions on fusion reactor materials are key phenomena to be understood to enable fusion as a feasible energy source for future reactors. We present significant improvements and validations of NEUTRO, a deterministic neutron transport code dedicated to solving the Boltzmann Transport Equation. The code is integrated as a module in the Alya system developed by the Barcelona Supercomputing Center and uses the Discrete Ordinates Method over an angular portion, multigroup for energy discretization and the Finite Element Method over unstructured meshes to treat special complex domains. Material anisotropy of the scattering medium is introduced into the scattering kernel using real base expressions for spherical harmonics. In order to build the total cross-section and the respective group matrix for the elastic cross-section, we use the NJOY code. We test the solver using different geometries and materials with varying levels of scattering properties. We compare our results on classic tests, benchmarks obtained from a Nuclear Energy Agency database and test cases using other neutron transport codes.

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Composite finite element solutions for neutron transport

Cited by 9 publications

References 14 publications

Angular adaptivity with spherical harmonics for Boltzmann transport

Angular adaptivity with spherical harmonics for Boltzmann transport

Goal-based angular adaptivity applied to the spherical harmonics discretisation of the neutral particle transport equation

Validating NEUTRO, a deterministic finite element neutron transport solver for fusion applications, with literature tests, experimental benchmarks and other neutronic codes

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