# Rhie-Chow interpolation

(Difference between revisions)
 Revision as of 11:39, 23 October 2005 (view source)Zxaar (Talk | contribs)← Older edit Latest revision as of 06:14, 27 August 2012 (view source)Michail (Talk | contribs) (5 intermediate revisions not shown) 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
:$H = \sum\limits_{neighbours} {a_l } \vec v_l$
:$H = \sum\limits_{neighbours} {a_l } \vec v_l$
- This interpolation of variables H and ${\nabla p}$ based on coefficients $a_p$ for pressure velocity coupling is called Rhie-Chow interpolation. + This interpolation of variables H and ${\nabla p}$ based on coefficients $a_p$ for [[Velocity-pressure coupling | pressure velocity coupling ]] is called Rhie-Chow interpolation. + + the Rhie-Chow interpolation is the same as adding a pressure term, which is proportional to a third derivative of the pressue ---- ----

## Latest revision as of 06:14, 27 August 2012

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.

the Rhie-Chow interpolation is the same as adding a pressure term, which is proportional to a third derivative of the pressue