4.9.3 Modeling Turbulent Diffusive Transport

$D_{T,ij}$ can be modeled by the generalized gradient-diffusion model of Daly and Harlow [ 67]:

However, this equation can result in numerical instabilities, so it has been simplified in ANSYS FLUENT to use a scalar turbulent diffusivity as follows [ 194]:

The turbulent viscosity, $\mu_t$, is computed using Equation  4.9-33.

Lien and Leschziner [ 194] derived a value of $\sigma_{k}= 0.82$ by applying the generalized gradient-diffusion model, Equation  4.9-2, to the case of a planar homogeneous shear flow. Note that this value of $\sigma_{k}$ is different from that in the standard and realizable $k$- $\epsilon$ models, in which $\sigma_{k} = 1.0$.