# RNG-LES model

(Difference between revisions)
 Revision as of 23:44, 18 September 2005 (view source)Zxaar (Talk | contribs)← Older edit Latest revision as of 06:27, 27 September 2005 (view source)Zxaar (Talk | contribs) Line 5: Line 5: The function $H\left( x \right)$ is defined as:
The function $H\left( x \right)$ is defined as:
- :$- H\left( x \right) - \begin{matrix} - = x - \begin{matrix} - {} & ; & {x > 0} \\ - \end{matrix} - \\ - = 0 - \begin{matrix} - {} & ; & {x \le 0} \\ - \end{matrix} - \end{matrix} + [itex] -$ + H\left( x \right) = \left\{ + + \begin{matrix} + + + {x  } & { ; } & {x  > 0}  \\ + {0  } & { ; } & {x  \le 0}  \\ + + + + \end{matrix} + + + \right. + [/itex]

- x is given by $+ '''x''' is given by [itex] x = {{\mu _s \mu _{eff} } \over {\mu ^3 }} - C x = {{\mu _s \mu _{eff} } \over {\mu ^3 }} - C$ [/itex] - Where ${C = 100}$ and $\mu _s$ is given by:
+ Where '''${C = 100}$''' and '''$\mu _s$''' is given by:
:$:[itex] \mu _s = \rho \left[ {C_{rng}} Vol^{1/3} \right]^{2} \begin{vmatrix} S \end{vmatrix} \mu _s = \rho \left[ {C_{rng}} Vol^{1/3} \right]^{2} \begin{vmatrix} S \end{vmatrix}$ [/itex]

- Where $C_{rng}$ is given by
+ Where '''$C_{rng}$''' is given by
:$:[itex] {C_{rng} = 0.157} {C_{rng} = 0.157}$ [/itex]

## Latest revision as of 06:27, 27 September 2005

Based on Renormalization Group Theory.
Here $\mu _{eff} = \mu \left[ {1 + H\left( x \right)} \right]^{1/3}$ .
The function $H\left( x \right)$ is defined as:

$H\left( x \right) = \left\{ \begin{matrix} {x } & { ; } & {x > 0} \\ {0 } & { ; } & {x \le 0} \\ \end{matrix} \right.$

x is given by $x = {{\mu _s \mu _{eff} } \over {\mu ^3 }} - C$

Where ${C = 100}$ and $\mu _s$ is given by:

$\mu _s = \rho \left[ {C_{rng}} Vol^{1/3} \right]^{2} \begin{vmatrix} S \end{vmatrix}$

Where $C_{rng}$ is given by

${C_{rng} = 0.157}$