IMPROVING A POSTERIORI SPATIAL DISCRETIZATION ERROR ESTIMATION FOR SN TRANSPORT BY SINGULAR CHARACTERISTICS TRACKING

Nathan H Hart,Yousry Y Azmy,M Margulis,P Blaise

doi:10.1051/epjconf/202124703022

Nathan H Hart, Yousry Y Azmy + Show 2 more

Open Access

https://doi.org/10.1051/epjconf/202124703022

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Abstract

Previously, we have developed a novel spatial discretization error estimator, the “residual source” estimator, in which an error transport problem, analogous to the discretized transport equation, is solved to acquire an estimate of the error, with a residual term acting as a fixed source. Like all error estimators, the residual source estimator suffers inaccuracy and imprecision in the proximity of singular characteristics, lines across which the solution is irregular. Estimator performance worsens as the irregularities become more pronounced, especially so if the true solution itself is discontinuous. This work introduces a modification to the residual approximation procedure that seeks to reduce the adverse effects of the singular characteristics on the error estimate. A partial singular characteristic tracking scheme is implemented to reduce the portion of the error in the numerical solution born by irregularities in the true solution. This treated numerical solution informs the residual approximations. The partial singular characteristic tracking scheme greatly enhances the numerical solution for a problem with prominent singular characteristics. The residual approximation and resultant residual source error estimate are likewise improved by the scheme, which only incurs the computational cost of an extra inner iteration.

Highlights

Applying a spatial discretization scheme to the SN neutral particle transport equation incurs a departure from the spatial-continuum solution, known as the spatial discretization error
Using the DGFEM-0/partial SCT” (pSCT) numerical solution to generate the residual yields the plots shown in Fig. 5 for the same problem
Two primary issues related to SCs have been identified in generating an LeR/TE-AD estimate: poor approximation of the TE-AD residual on SC-intersected cells due to deficiencies in the Taylor expansion representation of the true solution, and insufficiently accurate numerical solutions from spread of error from SCs resulting in poor high-order derivative approximations

Summary

Introduction

Applying a spatial discretization scheme to the SN neutral particle transport equation incurs a departure from the spatial-continuum solution, known as the spatial discretization error. Code users assume the spatial discretization, characterized by mesh size and method order/type, is sufficient to keep the error small. The field of a posteriori spatial discretization error estimation seeks to compute this quantity without knowledge of the true solution, generally for the purpose of adaptive mesh refinement (AMR) or error analysis, using the numerical solution in question to construct the estimate. We have rigorously pursued an accurate and precise implicit, residual-based error estimate known as the “residual source estimator” (LeR), and tested it for piecewise constant We performed parametric assessments of LeR, an h-refinement estimator [3], and an explicit, residual-based error bound [4], on a suite of Method of Manufactured Solutions (MMS) test cases that allow for analytical computation of the true solution [1,2]

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