Smagorinsky term in SGS kinetic energy equation -- CFD Online Discussion Forums

January 21, 2013, 09:15	Smagorinsky term in SGS kinetic energy equation	#1
Ivan New Member Ivan Join Date: Aug 2012 Posts: 22 Rep Power: 13	Dear all, I want to model the equation for the SGS turbulent kinetic energy (TKE) in LES context. Without entering the details, I have two terms I am dealing with. The first is the triple correlation (a) 1/2( $\overline{u_i u_i u_j}$ - $\overline{u_i u_i} \bar{u_j}$ ) which I model as crhodeltasqrt(k)*dk/dt, where k is the SGS TKE and c is a certain constant, and i put together with the diffusion term. All ok until here. There is, however, the term (b) $\frac{\partial}{\partial x_j} (\tau^r_{ij} u_i)$ where $\tau^r_{ij}$ is the residual term of the momentum equation, modelled as (c) $\tau^r_{ij} = -2\mu_t\bar{S}_{ij}$ My code follows a finite volume approach. I do not know then how to calculate this term (b). For example, is there a easy way to insert this term into the diffusion term? How this term is usually modelled (ex. implicitely or explicitely)?. Is there some paper to look at? Hope someone can help!

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