BACKSCATTER FROM A SCALE-SIMILARITY MODEL: EMBEDDED LES OF CHANNEL FLOW, DEVELOPING BOUNDARY LAYER FLOW AND BACKSTEP FLOW

Abstract

The scale-similarity model was proposed by Bardina et al. (1980) some 30 years ago. It was found not to be sufficiently dissipative. Much later, Davidson (2009) found a way to make it strictly dissipative. This was simply achieved by selecting those instants when the scale-similarity term in the momentum equation has the same sign as the viscous diffusive term (the latter term is indeed dissipative). In Davidson (2009) this technique was also used the other way around: by selecting time instants when the scale-similarity term has the opposite sign to the viscous diffusion term it acts as a backscatter term, which destabilizes the momentum equation. This feature is exploited in the present work to promote the generation of resolved turbulence. It is used to promote the creation of resolved turbulence in embedded LES of channel flow, and LES of developing boundary layer and backstep flow. The present method reduces the gray area problem described by Spalart (2009). The proposed method can also be used to promote transition from laminar to turbulent flow. 1 BACKSCATTER FROM THE SCALESIMILARITY MODEL The momentum equations for LES, with a turbulent viscosity and an additional SGS stress tensor, τik, from the scale-similarity model, read Dūi Dt + 1 ρ ∂ p ∂xi = ∂ ∂xk ( (ν + νSGS) ∂ ūi ∂xk )