Smagorinsky

Properties

Model equations

The turbulence viscosity is given by:

$$\nu_t = C_k \Delta k^{0.5}$$

where the turbulence kinetic energy is given by the solution of the quadratic equation:

$$a k^2 + b k + c = 0$$

The coefficients are:

$$\begin{aligned} a &= \frac{C_e}{\Delta} \\ b &= \frac{2}{3} \mathrm{tr} (\tensor{D}) \\ c &= 2 C_k \Delta \left( \mathrm{dev}(\tensor{D}) \ddprod \tensor{D} \right) \end{aligned}$$

and

$$\tensor{D} = \frac{1}{2} \left( \grad \u + \grad (\u)^T \right)$$

Default model coefficients

$C_e$	$C_k$

1.048 |      0.094

Initialisation

Usage

The model is specified using:

LES
{
    turbulence      on;
    LESModel        Smagorinsky;
}

Boundary conditions

Inlet

• fixedValue

Outlet

• Constrained outlet

Walls

• wall functions

Further information

Source code:

• Foam::LESModels::Smagorinsky

References:

• Smagorinsky 64