# Approximation Schemes for convective term - structured grids - definitions

### From CFD-Wiki

(→definitions for NV diagram) |
(→definitions for NV diagram) |
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we discovered such definitions as | we discovered such definitions as | ||

- | <math>\boldsymbol{ \hat{\ | + | <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> | <math>\boldsymbol{ \hat{\phi_{w}} }</math> is a function of <math>\boldsymbol{ \hat{\phi}_{W}} </math> |

## Revision as of 22:11, 29 September 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

## Usual using 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