Density in the governing equations

Ruonan · Post by **Ruonan** » Thu Apr 28, 2022 4:52 pm

Dear developers,

Could you please help to confirm the form of the momentum equation in Code_Saturne?

$\frac{\partial\vec{u}}{\partial t}+\vec{u}\cdot\vec{\nabla}\vec{u}=-\frac{\vec{\nabla}P}{\rho_0}+{\upsilon}\vec{\nabla}^2\vec{u}$

or

${\rho_0}\frac{\partial\vec{u}}{\partial t}+{\rho_0}\vec{u}\cdot\vec{\nabla}\vec{u}=-{\vec{\nabla}P}+{\rho_0}{\upsilon}\vec{\nabla}^2\vec{u}$

Because I want to add a centrifugal buoyancy source term in the momentum equation. I want to make sure whether to add $(1-\frac{\rho}{\rho_0}){\vec{\Omega}}\times({\vec{\Omega}}\times{\vec{r})$ or $({\rho_0}-{\rho}){\vec{\Omega}}\times({\vec{\Omega}}\times{\vec{r})$ , depending on which form the momentum equation is.

Thank you!

Bonne journée,
Ruonan

Post by **Yvan Fournier** » Fri Apr 29, 2022 2:46 pm

Hello,

I do not think we use adimensioned equations, so the second option would be correct (though i invite you to check on a verification case with rho much greater that or much smaller than 1 once you have added your term).

I'll let others more expert in the numerical aspects of the code correct me if needed.

Best regards,

Yvan

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Density in the governing equations

Density in the governing equations

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