Dynamic k-Equation Model for LES of Compressible Flows

The sub-grid scale (SGS) kinetic energy (KE) has to be modeled in LES of compressible flows. Standard compressible versions of the dynamic Smagorinsky model (DSM) use Yoshizawa's expression for SGS KE. However, it is well known that Yoshizawa's Model tends to under-predict the magnitude of SGS KE. Obtaining the SGS KE from its transport equation,has shown improved performance for incompressible flows (e.g. Ghosal {\it et al.} 1995, Kim \& Menon 1996). We develop a compressible version of the DSM model with SGS KE equation. The SGS KE transport equation for compressible flow is derived, and the unclosed terms in the compressible KE equation are modeled and dynamically closed using the Germano identity. The proposed model is applied to decaying isotropic turbulence and normal shock/isotropic turbulence interaction.