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clementolivier April 4, 2013 11:36

psi in compressibleInterFoam (OpenFoam)
Hi everyone,

I am currently using the solver compressibleInterFoam (of OpenFoam). I am trying to change the equation of state perfectFluid and therefore, I need to understand what is psi. It seems to be the compressibility defined by
\psi = \left( \frac{\partial \rho}{\partial p} \right)_T
But I am not sure at all.
Moreover, I do not understand the file pEqn.H, and thus it do not help me to understand how psi is used.

If someone could give me some help, I would be very thankful

Best regards


dalaron May 28, 2013 06:44

Hi Clement,

Have you managed to figure this out? I am also looking to implement an equation of state and am not sure what to make of the psi term.

Referring to the documentation for totalPressure boundary condition (which is more in line with my own interests), psi is defined as compressibility and has units m^2/s^2. Beyond that though, I have not seen any documentation about what it actually is ...

Continuing with the dimensional line of thought,
\psi = \frac{P}{\rho} = \frac{kg/ms^2}{kg/m^2}=\frac{m^2}{s^2}
so the units work out in that regard.


RaghavendraRohith April 24, 2014 09:08


I think the compressibility is actually the reverse that is being defined above. It is

psi = rho/p which makes it a isothermal compressibility


fanny February 9, 2016 07:52

totalPressure definition

In totalPressureFvPatchScalarField.H we can read that for compressible supersonic flow the total pressure is defined as :

\f[ p_p = \frac{p_0}{(1 + 0.5 \psi G |U|^2)^{\frac{1}{G}}}
p_p | pressure at patch [Pa]
p_0 | total pressure [Pa]
\gamma | ratio of specific heats (Cp/Cv)
\psi | compressibility [m2/s2]
G | coefficient given by \f$\frac{\gamma}{1-\gamma}\f$

What compressibility is ? is its dimension really m2/s2 ? and really not s2/m2 ??.
I would expect s2/m2 in order to obtain psi*U^2 as an unidimensional number ..

I am also surprised by the G definition. It is really \frac{\gamma}{1-\gamma} ?
I would expect the inverse frac{1-\gamma}{\gamma} ?

Does someone has an opinion on it?


RaghavendraRohith February 12, 2016 04:51


I see it is s2/m2 because in the above equation it is multiplied by U2 to get a scalar value.

Best Regards,

acs November 21, 2016 10:17

from the Programmer's Guide v 3.0.1
Hi, everyone,

If it still can help anybody, in studying the Programmer's Guide OF v. 3.0.1, I,ve found, in section 3.4, the definition of psi (\psi):
\psi = \frac{\partial \rho}{\partial p},
which is called the barotropic relationship (compressibility), and its unit is s²/m² (at least for sonicLiquidFoam).

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