Smagorinsky

Table of Contents

• Properties
• Model equations
• Default model coefficients
• Initialisation
• Usage
• Boundary conditions
• Further information

Note

Under construction - please check again later

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:

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

and

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

Default model coefficients

\( C_e \) | \( C_k \) ---------—|---------— 1.048 | 0.094

Initialisation

Usage

The model is specified using:

LES
{
    turbulence      on;
    LESModel        Smagorinsky;
}

Boundary conditions

Inlet

• Fixed value

Outlet

• Constrained outlet

Walls

• wall functions

Further information

Source code:

• Foam::LESModels::Smagorinsky

References:

• Smagorinsky [68]

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