Ackroyd

Ainsworth

Andrew G. Buchan

Aussourd

Baker

Bangerth

Buchan

Burgarelli

Christopher C. Pain

Christopher M.J. Baker

Farrell

Fournier

Frey

Gago

Jessee

Kelly

Lathouwers

Lewis

Mark A. Goffin

Matthew D. Eaton

Mirza

Oden

Pain

Park

Paul N. Smith

Pierce

Power

Ragusa

Rannacher

Rivara

Turcksin

Verfürth

Wang

Zhang

Zienkiewicz

Journal of Computational Physics

This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, keff, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for keff with directional dependence. General error estimators are derived for any given functional of the flux and applied to keff to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The keff goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained

Goffin, MA

Baker, CMJ

Buchan, AG

Pain, CC

Eaton, MD

Smith, PN

Spiral - Imperial College Digital Repository

Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes

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http://spiral.imperial.ac.uk/bitstream/10044/1/13879/2/Journal%20of%20Computational%20Physics_242_2013.pdf

Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes

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