Grid Convergence Error Analysis for Mixed-Order Numerical Schemes

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Review and assessment of turbulence models for hypersonic flows (2006, background): “Grid convergence error estimates for hypersonic flows are complicated by the presence of shock waves, which tend to reduce the spatial order of accuracy to first order on sufficiently refined meshes [23,24], regardless of the nominal order of the spatial discretization scheme.”
Review of code and solution verification procedures for computational simulation (2005, background): “It was shown by Roy [28] that the error in the GCI relative to the RDE band is given by The error in the GCI relative to the RDE band is thus an ordered error, meaning that it is reduced with mesh reﬁnement (i.e., as h !”
An improved k‐ ϵ model applied to a wind turbine wake in atmospheric turbulence (2015, methodology): “The discretization error ǫn of each grid leveln is estimated using a mixed order analysis [39]: ǫn = fn − fh→0 = g1hn + g2h2n + g3h3n +O(h4n), (16) wherefn is the grid solution,fh→0 is the extrapolated solution for an infinitely small grid siz ehn andg1, g2, g3 are the unknown constants to be evalua”