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Title: Spatial goal-based error estimation and adaptive mesh refinement (AMR) for diamond difference discrete ordinate (DD-SN) methods
Author: Jeffers, Rebecca Siân
ISNI:       0000 0004 6061 6974
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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A derivation of the dual weighted residual (DWR) goal-based error estimator is given for the 1-D DD-SN discretisation of the fixed source and eigenvalue neutron transport equations. The quantity of interest (QoI) is linear and non-linear respectively. Isotropic scattering is assumed. Error correction and adaptive mesh refinement (AMR) were implemented for the 1-D code to reduce the error in the QoI as a function of the number of degrees of freedom (DoF) required for the forward solution. Higher order DD methods in the 1-D code allowed for h, p and hp AMR. Cell-wise DWRs were used to select cells for refinement. In the hp case, a merit function was used to choose between h or p refinement for a given cell. The extension of the weighted residual (WR) view of the traditional 1-D DD-SN equations to multidimensions results in a bilinear/trilinear approximation within the cell and cell vertex values as unknowns. However, traditional DD codes express the unknowns as cell-average and cell-edge average fluxes. The bilinear and trilinear components of the flux within a cell cannot be recovered from these values for use in the DWR calculation. Two 2-D codes were written, one keeping the cell-vertex values as unknowns and the other implementing the traditional DD scheme. In the former the DWR is calculated as in the 1-D case. The flux result of the latter is mapped into a discontinuous finite element space with a zero bilinear term before calculating the DWR. The vertex code provided the best error estimates. The DWR error estimate had, in general, the same convergence rate as the reference error, though the effectivity index tended towards unity only for fixed source problems with high scatter ratios. The equivalence between the vertex method and the traditional DD method means that the SPN acceleration scheme used by EDF can still be applied.
Supervisor: Eaton, Matthew ; Bluck, Michael Sponsor: Engineering and Physical Sciences Council (EPSRC) ; EDF Energy
Qualification Name: Thesis (D.Eng.) Qualification Level: Doctoral