A new dynamic formula for determining the coefficient of Smagorinsky model

The most common method to determine the coefficient of Smagorinsky model now is to employ the Germano identity, however it is too complex and expensive in numerical calculation. In this letter we propose a new dynamic formula for determining the coefficient, which is based on the Kolmogorov equation of filtered velocity in physical space. The simplified formula is quite easy to implement in calculation. It is then verified in both homogeneous isotropic turbulence and wall-bounded turbulence by A Priori and A Posteriori tests.