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Quadratic inner element subgrid scale discretisation of the Boltzmann transport equation. / Baker, C. M.J.; Buchan, A. G.; Pain, C. C.; Tollit, B.; Eaton, M. D.; Warner, P.

In: Annals of Nuclear Energy, Vol. 45, 01.07.2012, p. 124-137.

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Baker, C. M. J., Buchan, A. G., Pain, C. C., Tollit, B., Eaton, M. D., & Warner, P. (2012). Quadratic inner element subgrid scale discretisation of the Boltzmann transport equation. Annals of Nuclear Energy, 45, 124-137. https://doi.org/10.1016/j.anucene.2012.02.020

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Baker, C. M.J. ; Buchan, A. G. ; Pain, C. C. ; Tollit, B. ; Eaton, M. D. ; Warner, P. / Quadratic inner element subgrid scale discretisation of the Boltzmann transport equation. In: Annals of Nuclear Energy. 2012 ; Vol. 45. pp. 124-137.

Bibtex

@article{36bba4d196e749cd8262e62c3a552813,
title = "Quadratic inner element subgrid scale discretisation of the Boltzmann transport equation",
abstract = "This paper explores the application of the inner element subgrid scale method to the Boltzmann transport equation using quadratic basis functions. Previously, only linear basis functions for both the coarse scale and the fine scale were considered. This paper, therefore, analyses the advantages of using different coarse and subgrid basis functions for increasing the accuracy of the subgrid scale method. The transport of neutral particle radiation may be described by the Boltzmann transport equation (BTE) which, due to its 7 dimensional phase space, is computationally expensive to resolve. Multi-scale methods offer an approach to efficiently resolve the spatial dimensions of the BTE by separating the solution into its coarse and fine scales and formulating a solution whereby only the computationally efficient coarse scales need to be solved. In previous work an inner element subgrid scale method was developed that applied a linear continuous and discontinuous finite element method to represent the solution's coarse and fine scale components. This approach was shown to generate efficient and stable solutions, and so this article continues its development by formulating higher order quadratic finite element expansions over the continuous and discontinuous scales. Here it is shown that a solution's convergence can be improved significantly using higher order basis functions. Furthermore, by using linear finite elements to represent coarse scales in combination with quadratic fine scales, convergence can also be improved with only a modest increase in computational expense.",
keywords = "Finite elements, Neutron transport, Subgrid scale",
author = "Baker, {C. M.J.} and Buchan, {A. G.} and Pain, {C. C.} and B. Tollit and Eaton, {M. D.} and P. Warner",
year = "2012",
month = "7",
day = "1",
doi = "10.1016/j.anucene.2012.02.020",
language = "English",
volume = "45",
pages = "124--137",
journal = "Annals of Nuclear Energy",
issn = "0306-4549",
publisher = "Elsevier Ltd",

}

RIS

TY - JOUR

T1 - Quadratic inner element subgrid scale discretisation of the Boltzmann transport equation

AU - Baker, C. M.J.

AU - Buchan, A. G.

AU - Pain, C. C.

AU - Tollit, B.

AU - Eaton, M. D.

AU - Warner, P.

PY - 2012/7/1

Y1 - 2012/7/1

N2 - This paper explores the application of the inner element subgrid scale method to the Boltzmann transport equation using quadratic basis functions. Previously, only linear basis functions for both the coarse scale and the fine scale were considered. This paper, therefore, analyses the advantages of using different coarse and subgrid basis functions for increasing the accuracy of the subgrid scale method. The transport of neutral particle radiation may be described by the Boltzmann transport equation (BTE) which, due to its 7 dimensional phase space, is computationally expensive to resolve. Multi-scale methods offer an approach to efficiently resolve the spatial dimensions of the BTE by separating the solution into its coarse and fine scales and formulating a solution whereby only the computationally efficient coarse scales need to be solved. In previous work an inner element subgrid scale method was developed that applied a linear continuous and discontinuous finite element method to represent the solution's coarse and fine scale components. This approach was shown to generate efficient and stable solutions, and so this article continues its development by formulating higher order quadratic finite element expansions over the continuous and discontinuous scales. Here it is shown that a solution's convergence can be improved significantly using higher order basis functions. Furthermore, by using linear finite elements to represent coarse scales in combination with quadratic fine scales, convergence can also be improved with only a modest increase in computational expense.

AB - This paper explores the application of the inner element subgrid scale method to the Boltzmann transport equation using quadratic basis functions. Previously, only linear basis functions for both the coarse scale and the fine scale were considered. This paper, therefore, analyses the advantages of using different coarse and subgrid basis functions for increasing the accuracy of the subgrid scale method. The transport of neutral particle radiation may be described by the Boltzmann transport equation (BTE) which, due to its 7 dimensional phase space, is computationally expensive to resolve. Multi-scale methods offer an approach to efficiently resolve the spatial dimensions of the BTE by separating the solution into its coarse and fine scales and formulating a solution whereby only the computationally efficient coarse scales need to be solved. In previous work an inner element subgrid scale method was developed that applied a linear continuous and discontinuous finite element method to represent the solution's coarse and fine scale components. This approach was shown to generate efficient and stable solutions, and so this article continues its development by formulating higher order quadratic finite element expansions over the continuous and discontinuous scales. Here it is shown that a solution's convergence can be improved significantly using higher order basis functions. Furthermore, by using linear finite elements to represent coarse scales in combination with quadratic fine scales, convergence can also be improved with only a modest increase in computational expense.

KW - Finite elements

KW - Neutron transport

KW - Subgrid scale

UR - http://www.scopus.com/inward/record.url?scp=84860430828&partnerID=8YFLogxK

U2 - 10.1016/j.anucene.2012.02.020

DO - 10.1016/j.anucene.2012.02.020

M3 - Article

AN - SCOPUS:84860430828

VL - 45

SP - 124

EP - 137

JO - Annals of Nuclear Energy

JF - Annals of Nuclear Energy

SN - 0306-4549

ER -