Functional Modeling

Abstract

According to the conclusions of Chap. 3, in the quasi-isentropic low-Mach regime, almost the entire turbulent kinetic energy is contained in the solenoidal modes, and the kinetic energy dissipation is mostly due to the solenoidal dissipation. Therefore, for this regime it is reasonable to assume that compressibility effects can be neglected when deriving an effective subgrid-scale model. This fundamental assumption is the basis of functional modeling for compressible flows being rooted in a incompressible framework. After introducing the classical concept of eddy-viscosity, we present some functional subgrid-scale (SGS) models that have been used for compressible flows. The modeling of the isotropic part of the SGS tensor and of the turbulent heat flux is discussed later. Before concluding with a brief introduction to implicit modeling from the functional perspective, some techniques improving the performance of eddy-viscosity models are detailed.