[geth03]

hi all,

i searched up the forum about this issue, but could not find a satisfactory explanation.

i would like to know what the mass imbalance is in every iteration step for a steady state calculation with simpleFoam.

1.normally, for an incompressible, steady state case the continuity equation would be: div(U)=0. from the computational side this equation should be div(U)=r, meaning there should be a residual r in every iteration.

2. Integral of div(U) over a control volume is equal to integral over the bounding surface of this control volume when Gauss theorem is applied:
Integral(div(U))dV=Integral(U_f*vector_n)dS, further this Integral can be discretized for a polyhedra -> SumOverAllFaces(U_f*vector_n*faceArea). This sum should be 0 ideally, but will give a residual r for every iteration step, which could be viewed as the mass imbalance for each cell.
i want to compute and output exactly this value.

so the question is, what do i need to do to compute this mass imbalance.
i know that there is the postprocessing utility "div". i did execute div(U) and div(phi) for icofoam. both values differ from each other (in this thread Meaning of "fvc::div(phi)" , post #20, it is claimed that both should give the same value). the dimension for both is 1/second.
i did calculate div(U) values with excel for this case manually, and got the same values which are shown in paraview.

i hope anybody can tell me how to compute the mass imbalance correctly.

[hjasak]

fvc::div(phi) is the right thing to do. If you need a smaller error, tighten the pressure solver tolerance.

Face flux phi is the face representation of the velocity field and this is what we apply the div(u) constraint on.

Hrv

[geth03]

Thank you Prof. Jasak.

What confuses me is that div(phi) has the dimension "per second" in the output-file. I don't know how to interpret that, do i need to multiply that value with the cell volume to get the volume flux imbalance and maybe that again with the density to get the mass imbalance in kg/second?

Thanks again for any advice.

[fly_light]

Hello geth03,

You can read the following two answers:
Meaning of "fvc::div(phi)"
the difference between div(U) and div(phi)

They already talked a lot.