A priori grid quality estimation for high-order finite differencing

Structured grids using the finite differencing method contain two sources of grid-induced truncation errors. The first is dependent on the solution field. The second is related only to the metrics of the grid transformation. The accuracy of the grid transformation metrics is affected by the inverse metrics, which are spatial derivatives of the grid in the generalised coordinates. The truncation errors contained in the inverse metrics are generated by the spatial schemes. Fourier analysis shows that the dispersion errors, by spatial schemes, have similarities to the transfer function of spatial filters. This similarity is exploited to define a grid quality metric that can be used to identify areas in the mesh that are likely to generate significant grid-induced errors. An inviscid vortex convection benchmark case is used to quantify the correlation between the grid quality metric and the solution accuracy, for three common geometric features found in grids: abrupt changes in the grid metrics, skewness, and grid stretching. A strong correlation is obtained, provided that the grid transformation errors are the most significant sources of error.

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