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

NC State University Dept. of Nuclear Engineering 2500 Stinson Dr., Raleigh, NC, USA 27607

nhhart@ncsu.edu
yyazmy@ncsu.edu

Published online: 22 February 2021

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.