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The accuracy of a large eddy simulation (LES) is determined by the accuracyof the model used to describe the effect of unresolved scales, the numericalerrors of the resolved scales, and the optimality of the length scale thatseparates resolved from unresolved scales (the filter-width, or thecoarse-graining length scale). This paper is focused entirely on the last ofthese, proposing a systematic algorithm for identifying the "optimal" spatialdistribution of the coarse-graining length scale and its aspect ratio. The coreidea is that the "optimal" coarse-graining length scale for LES is the largestlength scale for which the LES solution is minimally sensitive to it. This ideais formulated based on an error indicator that measures the sensitivity of thesolution and a criterion that determines how that error indicator should varyin space and direction to minimize the overall sensitivity of the solution. Thesolution to this optimization problem is that the cell-integrated errorindicator should be equi-distributed; a corollary is that one cannot link theaccuracy in LES to quantities that are not cell-integrated, including thecommon belief that LES is accurate whenever 80-90\% of the energy is resolved.The full method is tested on the wall-resolved LES of turbulent channel flowand the flow over a backward-facing step, with final length scale fields (orfilter-width fields, or grids) that are close to what is considered "bestpractice" in the LES literature. Finally, the derivation of the error indicatoroffers an alternative explanation for the success of the dynamic procedure.

Towards systematic grid selection in LES: iterative identification of the coarse-graining length scale by minimizing the solution sensitivity