# Approximation Schemes for convective term - structured grids - definitions

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and convected variable at face as <math> \boldsymbol{\phi_{f}} </math> | and convected variable at face as <math> \boldsymbol{\phi_{f}} </math> | ||

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+ | also you can find in literature such definition as <math> \boldsymbol{i+1/2} </math> , but we suggested it non suitable, because of complication | ||

== indicators of the local velocity direction == | == indicators of the local velocity direction == |

## Revision as of 17:51, 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

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) |