RNG-LES model

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(Difference between revisions)

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

${C_{rng} = 0.157}$

RNG-LES model

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Latest revision as of 06:27, 27 September 2005

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@@ Line 1: / Line 1: @@
-Based on Renormalization Group Theory.
+Based on Renormalization Group Theory.<br>
 Here <math>
 \mu _{eff}  = \mu \left[ {1 + H\left( x \right)} \right]^{1/3}
 </math> . <br>
-Where <math> H\left( x \right) </math> is given by: <br>
+The function <math> H\left( x \right) </math> is defined as: <br>
-:<math>
-H\left( x \right)
- \begin{matrix}
-= x
- \begin{matrix}
- {} & ; & {x > 0}  \\
- \end{matrix}
-\\
-= 0
- \begin{matrix}
-  {} & ; & {x \le 0}  \\
- \end{matrix}
-  \end{matrix}
+<math>
-</math>
+H\left( x \right)  = \left\{
+\begin{matrix}
+   {x  } & { ; } & {x  > 0}  \\
+   {0  } & { ; } & {x  \le 0}  \\
+\end{matrix}
+  \right.
+ </math>
 <br>
-x is given by <math>
+'''x''' is given by <math>
 x = {{\mu _s \mu _{eff} } \over {\mu ^3 }} - C
   </math>
-Where <math> {C = 100} </math> and <math>\mu _s </math> is given by: <br>
+Where '''<math> {C = 100} </math>''' and '''<math>\mu _s </math>''' is given by: <br>
 :<math>
 \mu _s  = \rho \left[ {C_{rng}} Vol^{1/3} \right]^{2} \begin{vmatrix} S \end{vmatrix}
+</math>
+<br>
+Where '''<math> C_{rng}  </math>''' is given by <br>
+:<math>
+{C_{rng}  = 0.157}
 </math>