CFD Online Discussion Forums - Having troubles in understanding the correction term in pressure equation

CFD Online Discussion Forums (https://www.cfd-online.com/Forums/)

- OpenFOAM (https://www.cfd-online.com/Forums/openfoam/)

- - Having troubles in understanding the correction term in pressure equation (https://www.cfd-online.com/Forums/openfoam/96556-having-troubles-understanding-correction-term-pressure-equation.html)

Having troubles in understanding the correction term in pressure equation

Hi,

I have troubles in understanding the correction term in pressure equation.
For example in buoyantPimpleFoam,

Code:

        

fvScalarMatrix p_rghDDtEqn

(

    fvc::ddt(rho) + psi*correction(fvm::ddt(p_rgh))

  + fvc::div(phi)

);

where does the term psi*correction(fvm::ddt(p_rgh)) come from?
It seems like it origins from the difference between old value and current value of rho. But how about if we write the eqn as

Code:

        

fvScalarMatrix p_rghDDtEqn

(

    fvc::ddt(psi,p) 

  + fvc::div(phi)

);

Back to the correction part, why there is no term like

Code:

        

 p_rgh*correction(fvc::ddt(psi))

Have you solved it?
I'm confused too. It should be related to the material differential of pressure, but I don't know how to get it in this particular form.