# Rhie-Chow interpolation

(Difference between revisions)
 Revision as of 00:06, 24 October 2005 (view source)Zxaar (Talk | contribs)← Older edit Revision as of 05:51, 24 October 2005 (view source)Zxaar (Talk | contribs) Newer edit → Line 1: Line 1: we have at each cell descretised equation in this form,
we have at each cell descretised equation in this form,
:$a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{{\nabla p}}{V}$ ;
:$a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{{\nabla p}}{V}$ ;
- :$\left[ {\frac{1}{{a_p }}H} \right]_{face} = \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face}$
+ For continuity we have
+ :$\sum\limits_{faces} \left[ {\frac{1}{{a_p }}H} \right]_{face} = \sum\limits_{faces} \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face}$
where
where

## Revision as of 05:51, 24 October 2005

we have at each cell descretised equation in this form,

$a_p \vec v_P = \sum\limits_{neighbours} {a_l } \vec v_l - \frac{{\nabla p}}{V}$ ;

For continuity we have

$\sum\limits_{faces} \left[ {\frac{1}{{a_p }}H} \right]_{face} = \sum\limits_{faces} \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face}$

where

$H = \sum\limits_{neighbours} {a_l } \vec v_l$

This interpolation of variables H and ${\nabla p}$ based on coefficients $a_p$ for pressure velocity coupling is called Rhie-Chow interpolation.