# Kinetic energy subgrid-scale model

### From CFD-Wiki

(Difference between revisions)

m (Reverted edits by CrochIvare (Talk) to last version by Salva) |
|||

(3 intermediate revisions not shown) | |||

Line 1: | Line 1: | ||

- | <math> k_{\rm sgs} = \frac{1}{2}\left(\overline{u_k^2} - \overline{u}_k^2 \right) </math> | + | The subgrid-scale kinetic energy is defined as <br> |

+ | :<math> k_{\rm sgs} = \frac{1}{2}\left(\overline{u_k^2} - \overline{u}_k^2 \right) </math> | ||

+ | |||

+ | |||

+ | The subgrid-scale stress can then be written as <br> | ||

+ | <math> \tau_{ij} - \frac{2}{3} k_{\rm sgs} \delta_{ij} =-2 C_k k_{\rm sgs}^{1/2} \Delta \overline{S}_{ij} </math> <br> | ||

+ | this gives us the transport equation for subgrid-scale kinetic energy <br> | ||

+ | <math> \frac{\partial \overline k_{\rm sgs}}{\partial t} + \frac{\partial \overline u_{j} \overline k_{sgs}} {\partial x_{j}} = - \tau_{ij} \frac{\partial \overline u_{i}}{\partial x_{j}} - C_{\varepsilon} \frac{k_{\rm sgs}^{3/2}}{\Delta} + \frac{\partial}{\partial x_{j}} \left( \frac{\mu_t}{\sigma_k} \frac{\partial k_{\rm sgs}}{\partial x_{j}} \right) </math> | ||

+ | |||

+ | |||

+ | |||

+ | The subgrid-scale eddy viscosity,<math> \mu_{t} </math>, is computed using <math> k_{\rm sgs} </math> as | ||

+ | |||

+ | |||

+ | <math> \mu_{t} = C_k k_{\rm sgs}^{1/2} \Delta </math> |

## Latest revision as of 09:46, 17 December 2008

The subgrid-scale kinetic energy is defined as

The subgrid-scale stress can then be written as

this gives us the transport equation for subgrid-scale kinetic energy

The subgrid-scale eddy viscosity,, is computed using as