# 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> | ||

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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,

- ;

For continuity we have

where

This interpolation of variables H and based on coefficients 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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