content_image/318319.jpg content_image/318318.jpg content_image/318317.jpg content_image/318316.jpg content_image/318315.jpg content_image/318312.jpg content_image/318314.jpg content_image/318313.jpg
where τ$_{ij}$ denotes the subgrid scale (SGS herefrom) stress tensor defined by 

<img src='content_image/318319.jpg'>

<img src='content_image/318318.jpg'>

The filtered equations are unclosed since the SGS stress tensor τ$_{ij}$ is unknown. The SGS stress tensor can be modelled based on an isotropic eddy-viscosity model as: 

<img src='content_image/318317.jpg'>

where ν$_{t}$ denotes the SGS eddy viscosity, and S$_{ij}$ is the resolved rate of strain tensor given by 

<img src='content_image/318316.jpg'>

where ν$_{t}$ is computed in terms of the Smagorinsky [31] type eddy-viscosity model using 

<img src='content_image/318315.jpg'>

where C$_{ν}$ denotes the Smagorinsky coefficient, | S | the modulus of rate of strain tensor for the resolved scales, 

and Δ denotes the grid filter length obtained from 

Consequently, the SGS stress tensor is computated as following 

<img src='content_image/318312.jpg'>

<img src='content_image/318314.jpg'>

<img src='content_image/318313.jpg'>

This model claims to be simple and efficient. It needs merely a constant in priori value for C$_{ν}$ . Nevertheless, work from [32, 33, 34] has shown different values of C$_{ν}$ for distinct flows. Hence, the 

