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October 6, 2009, 11:34 
understanding the term: fvm::Sp(fvc::div(phi), h)

#1 
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Dominik Christ
Join Date: Mar 2009
Posts: 28
Rep Power: 9 
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 

April 28, 2011, 11:37 

#2  
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Daniel P. Combest
Join Date: Mar 2009
Location: St. Louis, USA
Posts: 585
Rep Power: 20 
Quote:
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 

May 7, 2011, 05:53 

#3 
Member

Hi Dan, you mentioned that
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 

May 7, 2011, 08:14 

#4 
Member

Hi Foamers
again... about the div U =0... 'cause it's obviously correct in the simple singlephase 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 //Kai 

Tags 
energy equation, source term 
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