Goal-Based Error Estimation, Functional Correction, h, p and hp Adaptivity of the 1-D Diamond Difference Discrete Ordinate Method

摘要

This paper uses local dual weighted residual (DWR) error indicators to flag cells for goal-based refinement in a 1-D diamond difference (DD) discretisation of the discrete ordinate (S-N) neutron transport equations. Goal-orientated adaptive mesh refinement (GO-AMR) aims to produce a mesh that is optimal for a given goal or Qol (Quantity of Interest), h, p and hp refinement is implemented and applied to various test cases. A merit function is derived for the combined hp algorithm and is calculated for each refinement option within each flagged cell. The refinement option with the highest merit function is chosen for a given flagged cell. This paper also investigates the use of the DWR error estimation as a correction term for the originally calculated Qol. If error correction and GO-AMR are combined the DWR error indicators do not always give an optimal mesh for the corrected value of the Qol. Therefore, refinement indicators based on the error in the error correction term are used and tested in this work.