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Rhie-Chow interpolation

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we have at each cell descretised equation in this form, <br>
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> 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>
where <br>

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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