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Rhie-Chow interpolation

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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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  2. Solution of Navier-Stokes equation

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