The scale invariance properties of compressible Navier-Stokes and energy equations subject to density-weighted filtering are investigated, and the derived evolution equations for all required first and second order filtered moments provide the theoretical underpinning for variable-resolution calculations of reacting and compressible turbulent flows.

Flow, Turbulence and Combustion

The scale invariance properties of compressible Navier–Stokes and energy equations subject to density-weighted filtering are investigated. Scale or filter invariance forms of compressible moment equations require that two forms of generalized central second-order moments be defined—(1) product of two density-weighted sub-filter fluctuations and (2) product of one density-weighted and one un-weighted sub-filter fluctuation. The evolution equations for all required first and second order filtered moments are derived. These results provide the theoretical underpinning for variable-resolution calculations of reacting and compressible turbulent flows.

On the Invariance of Compressible Navier–Stokes and Energy Equations Subject to Density-Weighted Filtering