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September 13, 2012, 21:42 
Simple question about icoFoam

#1 
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Yuri Almeida
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The momentum equation in icoFoam.C (OF21) is the following: fvVectorMatrix UEqn ( fvm::ddt(U) + fvm::div(phi, U)  fvm::laplacian(nu, U) ); solve(UEqn == fvc::grad(p)); If I understood right, the equation would be: d(U)/dt + div(rho*U*U)  laplacian((mu/rho)*U) = grad(p) (1) But the equation found in books is: d(rho*U)/dt + div(rho*U*U)  laplacian(mu*U) = grad(p) (2) or, dividing by rho: d(U)/dt + div(U*U)  laplacian((mu/rho)*U) = (1/rho)*grad(p) (3) My question is: Why are equation 2 and 3 different from 1? Probably they are not, but, where is "rho" in fvc::grad(p) and why is it present in div(phi, U)?? Thx in advance! 

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September 14, 2012, 03:51 

#2  
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Gerhard Holzinger
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Hello,
in (1) you have rho in the convective term Quote:
d(U)/dt + div(U*U)  laplacian((mu/rho)*U) = grad(p) (1.1) Quote:
In an icoFoam case, the dimension of pressure is dimensions [0 2 2 0 0 0 0]; So, although in eq (1.1) and eq (3) the symbol p is used, the meaning of p is not the same in this equations. In icoFoam p is a pressure that's been divided by rho. 

September 14, 2012, 08:34 

#3 
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Yuri Almeida
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Hi Gerhard,
Now I got it, I knew that the equation was right, but I didn't understand how. So, phi is flux, this makes sense, however, I saw that phi = rho*U from here: http://www.openfoam.org/docs/user/fvSchemes.php "The divSchemes subdictionary contains divergence terms. Let us discuss the syntax of the entry in reference to a typical convection term found in fluid dynamics div(rhoUU), which in OpenFOAM applications is commonly given the identifier div(phi,U), where phi refers to the flux phi = rhoU." Thanks for the attention, Gerhard. 

September 14, 2012, 09:04 

#4 
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Gerhard Holzinger
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I see, maybe that is the case for compressible solvers. In an incomressible case rho is eliminated.


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