Rhie-Chow interpolation

(Difference between revisions)

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.

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Numerical Methods
Solution of Navier-Stokes equation

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 we have at each cell descretised equation in this form, <br>
 :<math> a_p \vec v_P  = \sum\limits_{neighbours} {a_l } \vec v_l  - \frac{{\nabla p}}{V} </math> ;  <br>
-:<math> \left[ {\frac{1}{{a_p }}H} \right]_{face}  = \left[ {\frac{1}{{a_p }}\frac{{\nabla p}}{V}} \right]_{face} </math> <br>
+For continuity we have <br>
+:<math> \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} </math> <br>
 where <br>