Correlation of grid quality metrics and solution accuracy for supersonic flows

It is well known that the quality of a computational grid can have a strong impact on the accuracy of solutions computed via CFD. For the past several years, there has been a drive to develop grid quality metrics that can be used a priori to predict the sufficiency of a given grid for a given simulation. Herein, a systematic study is detailed in which the supersonic flow over a diamond-wedge airfoil is computed with more than 50 structured grids. For each grid, a set of thirty grid quality metrics are computed as well as seven measures of solution accuracy. A statistical analysis of the results shows that there is essentially no correlation of the various quality metrics with solution accuracy. Hence, at least for the types of flows examined here, it appears that a priori grid quality metrics that correlate well with solution accuracy are not currently available.