The open source CFD toolbox
Smagorinsky

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# 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{align} 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{align}

and

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

# Default model coefficients

$$C_e$$ $$C_k$$
1.048 0.094

# Usage

The model is specified using:

LES
{
turbulence      on;
LESModel        Smagorinsky;
}


# Boundary conditions

Inlet

Outlet

Walls

• wall functions

# Further information

Source code:

References:

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