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RNG-LES model

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The function <math> H\left( x \right) </math> is defined as: <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}
 
-
\\
 
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= 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>
<br>
-
x is given by <math>
+
'''x''' is given by <math>
x = {{\mu _s \mu _{eff} } \over {\mu ^3 }} - C
x = {{\mu _s \mu _{eff} } \over {\mu ^3 }} - C
  </math>
  </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>  
:<math>  
\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}  
</math>  
</math>  
<br>
<br>
-
Where <math> C_{rng}  </math> is given by <br>
+
Where '''<math> C_{rng}  </math>''' is given by <br>
:<math>  
:<math>  
{C_{rng}  = 0.157}
{C_{rng}  = 0.157}
</math>
</math>

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}
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