Rhie-Chow interpolation

(Difference between revisions)

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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Numerical Methods
Solution of Navier-Stokes equation

@@ Line 1: / Line 1: @@
 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>
@@ Line 7: / Line 8: @@
 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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