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understanding the term: fvm::Sp(fvc::div(phi), h)

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Old   October 6, 2009, 11:34
Default understanding the term: fvm::Sp(fvc::div(phi), h)
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Dominik Christ
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Hello everyone,

when having a closer look at the energy equation as it is used by solvers for reacting cases, I cannot figure out where the term
- fvm::Sp(fvc::div(phi), h)
comes from. All I could find out is that it is a source term of some kind but when I try to derive an energy equation for enthalpy I do not get such a source term.

Could anybody please enlighten me? :-)

Thanks in advance!

Regards
Dominik
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Old   April 28, 2011, 11:37
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Quote:
Originally Posted by dominik_christ View Post
Hello everyone,

when having a closer look at the energy equation as it is used by solvers for reacting cases, I cannot figure out where the term
- fvm::Sp(fvc::div(phi), h)
comes from. All I could find out is that it is a source term of some kind but when I try to derive an energy equation for enthalpy I do not get such a source term.

Could anybody please enlighten me? :-)

Thanks in advance!

Regards
Dominik

Dominik,

I know this is an old thread, but I'm sure others run into it and have the same question. The origin of this term Sp(div(phi),h) comes from the expansion of the div(U,h) term in the transport equation.

div(U,h) = h*div(U) + U&grad(h).

In a completely converged domain the div(U) -> 0.

However, sometimes there is incomplete convergence and there is some generation (or consumption) that will throw off the energy balance. Have a look at

origin of fvm::Sp(fvc::div(phi_), epsilon_) in kepsilon Eqn?

and

ScalarTransportFoam for RTD calculations

for maybe a little explanation.

Dan
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Old   May 7, 2011, 05:53
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Hi Dan, you mentioned that

Quote:
Originally Posted by chegdan View Post
In a completely converged domain the div(U) -> 0.
which I cannot understand. For example, in an incompressible flow we may have div(U) = 0 everywhere. But how could you apply it to all the other cases? And what is the definition of U in you opinion? For example in two phase flow, will it be the velocity of each component or a mixed velocity? Or maybe there's no physics principle for div(U) = 0 at all? Is it a kind of restriction from mathematics? If possible, can you give me some references? Thx

// Kai
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Old   May 7, 2011, 08:14
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Hi Foamers

again... about the div U =0... 'cause it's obviously correct in the simple single-phase incompressible flow.

However if it comes to two phase flow, where there is a phase change term on RHS of eq. for instance in alphaEqn.H, it looks like
Code:
            ddt(alpha)
         + div(phi, alpha)           
           ==
           Gamma/rhoa
It is a kind of 1st order differential equations. alpha is bounded only if we have div(phi)=0, as the equation required. It seems that we cannot find any proof of div(phi)=0 directly from physics. All we can find come from the mathematical requirement. Any comments?

//Kai
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