# Approximation Schemes for convective term - structured grids - definitions

(Difference between revisions)
 Revision as of 14:34, 29 September 2005 (view source)Michail (Talk | contribs)← Older edit Revision as of 17:29, 29 September 2005 (view source)Michail (Talk | contribs) (→indicators of the local velocity direction)Newer edit → Line 26: Line 26: == indicators of the local velocity direction == == indicators of the local velocity direction == + + +
+ :$+ \phi_{w}=\sigma^{+}_{w}\phi_{W} + \sigma^{-}_{w}\phi_{P} +$ + (1)
+ + + where $\sigma^{+}_{w}$ and $\sigma^{-}_{w}$ are the indicators of the local velocity direction such that + + +
+ :$+ \sigma^{+}_{w} = 0.5 \left( 1 + \frac{\left|U_{w} \right|}{U_{w}} \right) +$ + (1)
+ +
+ :$+ \sigma^{-}_{w} = 1 - \sigma^{+}_{w} +$ + (1)
+ + and of course + +
+ $+ \left( U_{w} \neq 0 \right) +$ + (1)

## Revision as of 17:29, 29 September 2005

Here we shall develop a commone definitions and regulations because of

• in different articles was used defferent definitions and notations
• we are searching for common approach and generalisation

## Usual using definition for convected variable

$\boldsymbol{f}$

$\boldsymbol{\phi}$

## definition of considered face, upon wich approximation is applied

usually (in the most articles) west face of the control volume $\boldsymbol{w}$ is considered (without loss of generality)

for which flux is directed from the left to the right

we shall define it as $\boldsymbol{f}$

and convected variable at face as $\boldsymbol{\phi_{f}}$

## indicators of the local velocity direction

 $\phi_{w}=\sigma^{+}_{w}\phi_{W} + \sigma^{-}_{w}\phi_{P}$ (1)

where $\sigma^{+}_{w}$ and $\sigma^{-}_{w}$ are the indicators of the local velocity direction such that

 $\sigma^{+}_{w} = 0.5 \left( 1 + \frac{\left|U_{w} \right|}{U_{w}} \right)$ (1)
 $\sigma^{-}_{w} = 1 - \sigma^{+}_{w}$ (1)

and of course

 $\left( U_{w} \neq 0 \right)$ (1)