Grid Quality Measures for Iterative Convergence

TL;DR

This paper introduces two grid-quality measures, F- and G-measures, to evaluate and predict the iterative convergence behavior of unstructured-grid Navier-Stokes solvers for both inviscid and viscous flows.

Contribution

It defines and analyzes the F- and G-measures as new geometric criteria for assessing grid quality related to solver convergence.

Findings

Lower F-measure correlates with faster convergence

Smaller G-measure values indicate improved convergence towards zero

Measures are effective for both inviscid and viscous flow problems

Abstract

In this paper, we discuss two grid-quality measures, F- and G-measures, in relation to iterative convergence of an implicit unstructured-grid Navier-Stokes solver. The F-measure is a lower bound of a least-squares gradient, which is a purely geometrical quantity defined in each cell and thus can be computed for a given grid: faster convergence is expected for a grid with a lower value of the F-measure. The G-measure is a least-squares gradient of a specified function around each cell, with the minimum value of zero. Faster convergence is expected for a smaller value of the G-measure towards zero. In this paper, we investigate these measures for inviscid and viscous problems with unstructured grids in two dimensions.