Approximation Schemes for convective term - structured grids - definitions
From CFD-Wiki
(Difference between revisions)
(→indicators of the local velocity direction) |
(→indicators of the local velocity direction) |
||
Line 64: | Line 64: | ||
<math>U^{+}_{f}</math> and <math>U^{-}_{f}</math> | <math>U^{+}_{f}</math> and <math>U^{-}_{f}</math> | ||
+ | |||
+ | therefore unnormalised form of approximation scheme can be written | ||
+ | |||
+ | <table width="100%"><tr><td> | ||
+ | <math> | ||
+ | \phi_{f}=U^{+}_{f}\phi_{W} + U^{-}_{f}\phi_{P} | ||
+ | </math> | ||
+ | </td><td width="5%">(1)</td></tr></table> | ||
+ | |||
+ | or in more general form | ||
+ | |||
+ | <table width="100%"><tr><td> | ||
+ | <math> | ||
+ | \phi_{f}=U^{+}_{f}\phi_{C} + U^{-}_{f}\phi_{D} | ||
+ | </math> | ||
+ | </td><td width="5%">(1)</td></tr></table> |
Revision as of 17:49, 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
definition of considered face, upon wich approximation is applied
usually (in the most articles) west face of the control volume is considered (without loss of generality)
for which flux is directed from the left to the right
we shall define it as
and convected variable at face as
indicators of the local velocity direction
approximation scheme can be written in the next form
| (1) |
where and are the indicators of the local velocity direction such that
| (1) |
| (1) |
and of course
| (1) |
also used such definitions as and
we offer to use
and
therefore unnormalised form of approximation scheme can be written
| (1) |
or in more general form
| (1) |