The Filtering Grid Scale （FGS） of sub-grid scale models does not match with the theoretical Proper FGS （PFGS） because of the improper mesh. Therefore, proper Large Eddy Simulation （LES） Mesh is very decisive for better results and more economical cost. In this work, the purpose is to provide an adaptive control strategy for proper LES mesh with turbulence theory and CFD methods. A new expression of PFGS is proposed on the basis of -5/3 law of inertial sub-range and the proper mesh of LES can be built directly from the adjustment of RANS mesh. A benchmark of the backward facing step flow at Re = 5147 is provided for application and verification. There are three kinds of mesh sizes, including the RANS mesh, LAM （LES of adaptive-control mesh）, LFM （LES of fine mesh）, employed here. The grid number of LAM is smaller than those of LFM evidently, and the results of LAM are in a good agreement with those of DNS and experiments. It is revealed that the results of LAM are very close to those of LFM. The conclusions provide positive evidences for the novel strategy.
Without rational criteria to determine the Proper Sampled Data Scale （PSDS）, it would result in the expense of the too much unnecessary processing time and storage space in turbulent experiments. A novel approach for PSDS was established herein on the basis of turbulence theory and statistics. The specific procedure was given by using wavelet tools. A case study to prove the reliability and rationality of this approach was reported, where the sampled hot-wire data were from the experiment of square duct flow and turbulence kinetic energy was selected as the concerned turbulence parameter. It is shown that 2^20 quantities of the sampled data are enough to analyze turbulence kinetic energy in the present experiment. The PSDSs of three turbulence parameters at different Reynolds numbers （Re = 4.60×10^4, 7.68×10^4 and 1.23×10^5） were studied. The results illustrate that the PSDSs increase with the increment of the Reynolds number and the order of concerned turbulence parameter.
