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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>
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:<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>
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This interpolation of variables H and <math> {\nabla p} </math> based on coefficients <math> a_p </math> for [[Velocity-pressure coupling | pressure velocity coupling  ]] is called <b>Rhie-Chow interpolation</b>.
This interpolation of variables H and <math> {\nabla p} </math> based on coefficients <math> a_p </math> for [[Velocity-pressure coupling | pressure velocity coupling  ]] is called <b>Rhie-Chow interpolation</b>.
 +
 +
the Rhie-Chow interpolation is the same as adding a pressure term, which is proportional to a third derivative of the pressue
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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


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