Comment on "A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies" (L. Eça and M. Hoekstra, Journal of Computational Physics 262 (2014) 104-130)

Eça and Hoekstra [1] proposed a procedure for the estimation of the numerical uncertainty of CFD calculations based on the least squares root (LSR) method. We believe that the LSR method has potential value for providing an extended Richardson-extrapolation solution verification procedure for mixed monotonic and oscillatory or only oscillatory convergent solutions (based on the usual systematic grid-triplet convergence condition R). Current Richardson-extrapolation solution verification procedures [2–7] are restricted to monotonic convergent solutions 0 < R < 1. Procedures for oscillatory convergence simply either use uncertainty estimate based on average maximum minus minimum solutions [8,9] or arbitrarily large factors of safety (F S ) [2]. However, in our opinion several issues preclude the usefulness of the presented LSR method: five criticisms follow.