Approximation Schemes for convective term - structured grids - definitions
From CFD-Wiki
(→indicators of the local velocity direction) |
(→node stencil) |
||
(11 intermediate revisions not shown) | |||
Line 6: | Line 6: | ||
* we are searching for common approach and generalisation | * we are searching for common approach and generalisation | ||
- | == Usual | + | '''Please note:''' ''as we still developing this section, you can find the rest of non-unificated definitions'' |
+ | |||
+ | == Usual used definition for convected variable == | ||
<math> | <math> | ||
Line 14: | Line 16: | ||
<math> | <math> | ||
\boldsymbol{\phi} | \boldsymbol{\phi} | ||
- | </math> | + | </math> |
+ | |||
+ | we shall use here <math>\boldsymbol{\phi}</math> | ||
== definition of considered face, upon wich approximation is applied == | == definition of considered face, upon wich approximation is applied == | ||
- | usually (in the most articles) west face | + | usually (in the most articles) west face <math> |
- | \boldsymbol{w} </math> is considered | + | \boldsymbol{w} </math> of the control volume is considered ''without loss of generality'' |
+ | |||
+ | for which '''flux is directed from the left to the right''' i.e. <math> \boldsymbol{U_{f} \triangleright 0 } </math> | ||
- | |||
we shall define it as <math> \boldsymbol{f} </math> | we shall define it as <math> \boldsymbol{f} </math> | ||
Line 87: | Line 92: | ||
== definitions for NV diagram == | == definitions for NV diagram == | ||
+ | |||
+ | |||
+ | we discovered such definitions as | ||
+ | |||
+ | <math>\boldsymbol{ \hat{\phi}_{i+1/2} }</math> is a function of <math>\boldsymbol{ \hat{\phi}_{i}} </math> | ||
+ | |||
+ | <math>\boldsymbol{ \hat{\phi_{w}} }</math> is a function of <math>\boldsymbol{ \hat{\phi}_{W}} </math> | ||
+ | |||
+ | we shall use here | ||
+ | |||
+ | <math>\boldsymbol{ \hat{\phi_{f}} }</math> is a function of <math>\boldsymbol{ \hat{\phi}_{C}} </math> | ||
+ | |||
+ | == node stencil == | ||
+ | |||
+ | Bear in mind this stencil | ||
+ | |||
+ | |||
+ | |||
+ | ---- | ||
+ | <i> Return to [[Numerical methods | Numerical Methods]] </i> | ||
+ | |||
+ | <i> Return to [[Approximation Schemes for convective term - structured grids]] </i> |
Latest revision as of 01:14, 9 November 2005
Contents |
Goals of this section
Here we shall develop a commone definitions and regulations because of
- in different issues was used different definitions and notations
- we are searching for common approach and generalisation
Please note: as we still developing this section, you can find the rest of non-unificated definitions
Usual used definition for convected variable
we shall use here
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 i.e.
we shall define it as
and convected variable at face of CV as
also you can find in literature such definition as , but we suggested it non suitable, because of complication
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) |
definitions for NV diagram
we discovered such definitions as
is a function of
is a function of
we shall use here
is a function of
node stencil
Bear in mind this stencil
Return to Numerical Methods
Return to Approximation Schemes for convective term - structured grids