gradient of pressure

sharonyue · September 4, 2013, 04:37

Hi All,

In VOF, we have this equation:

${p_d} = p - \rho g \cdot h$

In the code, it reads:

$\nabla {p_d} = \nabla p - \rho g - g \cdot h\nabla \rho$

Well,Shouldn't it be

$\nabla {p_d} = \nabla p - g \cdot h\nabla \rho - \rho \nabla(g \cdot h)$ ?

sharonyue · September 8, 2013, 21:22

hello? no one is here

Sylv · September 11, 2013, 10:09

And in the source code, how it looks? Do you have a piece of code?

sharonyue · September 11, 2013, 19:58

Quote:

Originally Posted by Sylv

And in the source code, how it looks? Do you have a piece of code?

In interFoam's UEqn's code:

Code:

fvVectorMatrix UEqn
    (
        fvm::ddt(rho, U)
      + fvm::div(rhoPhi, U)
      + turbulence->divDevRhoReff(rho, U)
    );

    UEqn.relax();

    if (pimple.momentumPredictor())
    {
        solve
        (
            UEqn
         ==
            fvc::reconstruct
            (
                (
                    fvc::interpolate(interface.sigmaK())*fvc::snGrad(alpha1)
                  - ghf*fvc::snGrad(rho)
                  - fvc::snGrad(p_rgh)
                ) * mesh.magSf()
            )
        );
    }

Its:
$\nabla {p_d} = \nabla p - \rho g - g \cdot h\nabla \rho$

but why?

Sylv · September 16, 2013, 04:32

mmmh, I'm not familiar with interFoam, so I don't know the hypothesis involved in the design of this solver, and by extend, in the selection of the equations.

Regarding your first post, I agree with you, the following equation seems the right one: $\nabla {p_d} = \nabla p - g \cdot h\nabla \rho - \rho \nabla(g \cdot h)$ . BUT, as I said, it might have a dozen of hypothesis which explain the selection of the first equation.

What about validation and/or papers on interFoam? If the equations were really wrong, somebody should have noticed it. Look at this page, it might help you: http://openfoamwiki.net/index.php/InterFoam

Bernhard · September 16, 2013, 04:39

$\nabla(g\cdot h)=g$
There is no difference between the two, nor any underlying assumption, because

$\nabla( g\cdot h)=\nabla (g_x x + g_y y + g_z z) =(g_x, g_y, g_z)$ ,
only assuming that g is a constant.

sharonyue · September 16, 2013, 04:43

Quote:

Originally Posted by Sylv

mmmh, I'm not familiar with interFoam, so I don't know the hypothesis involved in the design of this solver, and by extend, in the selection of the equations.

Regarding your first post, I agree with you, the following equation seems the right one: $\nabla {p_d} = \nabla p - g \cdot h\nabla \rho - \rho \nabla(g \cdot h)$ . BUT, as I said, it might have a dozen of hypothesis which explain the selection of the first equation.

What about validation and/or papers on interFoam? If the equations were really wrong, somebody should have noticed it. Look at this page, it might help you: http://openfoamwiki.net/index.php/InterFoam

Thank you man, I think Bernhard is rite, its only math...
Thank you both.

September 16, 2013, 04:39		#6
Bernhard Senior Member Bernhard Join Date: Sep 2009 Location: Delft Posts: 790 Rep Power: 21	$\nabla(g\cdot h)=g$ There is no difference between the two, nor any underlying assumption, because $\nabla( g\cdot h)=\nabla (g_x x + g_y y + g_z z) =(g_x, g_y, g_z)$ , only assuming that g is a constant. sharonyue likes this.

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September 8, 2013, 21:22		#2
sharonyue Senior Member Dongyue Li Join Date: Jun 2012 Location: Beijing, China Posts: 838 Rep Power: 17	hello? no one is here

September 11, 2013, 10:09		#3
Sylv New Member Marcel Vonlanthen Join Date: Nov 2012 Location: Zurich, Switzerland Posts: 28 Rep Power: 13	And in the source code, how it looks? Do you have a piece of code?

September 16, 2013, 04:32		#5
Sylv New Member Marcel Vonlanthen Join Date: Nov 2012 Location: Zurich, Switzerland Posts: 28 Rep Power: 13	mmmh, I'm not familiar with interFoam, so I don't know the hypothesis involved in the design of this solver, and by extend, in the selection of the equations. Regarding your first post, I agree with you, the following equation seems the right one: $\nabla {p_d} = \nabla p - g \cdot h\nabla \rho - \rho \nabla(g \cdot h)$ . BUT, as I said, it might have a dozen of hypothesis which explain the selection of the first equation. What about validation and/or papers on interFoam? If the equations were really wrong, somebody should have noticed it. Look at this page, it might help you: http://openfoamwiki.net/index.php/InterFoam