Simple question about icoFoam
The momentum equation in icoFoam.C (OF21) is the following:
+ 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!
in (1) you have rho in the convective term
d(U)/dt + div(U*U) - laplacian((mu/rho)*U) = -grad(p) (1.1)
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.
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:
"The divSchemes sub-dictionary 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.
I see, maybe that is the case for compressible solvers. In an incomressible case rho is eliminated.
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