Approximation Schemes for convective term - structured grids - definitions

(Difference between revisions)

Revision as of 17:29, 29 September 2005

Here we shall develop a commone definitions and regulations because of

$\boldsymbol{f}$

$\boldsymbol{\phi}$

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 $\boldsymbol{\phi_{f}}$

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

(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)

@@ Line 26: / Line 26: @@
 == indicators of the local velocity direction ==
+<table width="100%"><tr><td>
+:<math>
+\phi_{w}=\sigma^{+}_{w}\phi_{W}	+ \sigma^{-}_{w}\phi_{P}
+</math>
+</td><td width="5%">(1)</td></tr></table>
+where <math>\sigma^{+}_{w}</math> and <math>\sigma^{-}_{w}</math> are the indicators of the local velocity direction such that
+<table width="100%"><tr><td>
+:<math>
+\sigma^{+}_{w} = 0.5 \left( 1 + \frac{\left|U_{w} \right|}{U_{w}} \right)
+</math>
+</td><td width="5%">(1)</td></tr></table>
+<table width="100%"><tr><td>
+:<math>
+\sigma^{-}_{w} = 1 - \sigma^{+}_{w}
+</math>
+</td><td width="5%">(1)</td></tr></table>
+and of course
+<table width="100%"><tr><td>
+<math>
+\left( U_{w} \neq 0  \right)
+</math>
+</td><td width="5%">(1)</td></tr></table>