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"Counter-gradient" term in interFoam.

Hi guys,

Some articles depict the interFoam in detail, but I still have many confusions. In weller's paper: he said:

Quote:

$\frac{{\partial \alpha }}{{\partial t}} + \nabla \cdot \alpha u + \nabla \cdot \left( {\alpha \left( {1 - \alpha } \right){u_c}} \right) = 0$

U_c ensures compression. In order to ensure the compression term does not bias the solution in anyway it should only introduce flow of alpha normal to the interface, in the direction: $\frac{{\nabla \alpha }}{{\left| {\nabla \alpha } \right|}}$
......
These considerations suggest a model for Uc of the form
${U_c} = {c_\alpha }\left| U \right|\frac{{\nabla \alpha }}{{\left| {\nabla \alpha } \right|}}$

So according to Weller's thought, U_c is constructed by a guess.

but in another paper. it said:

Quote:

All in all, how can we ensure these two U_c are the same?

The first one is the one that is implemented in OpenFOAM, as you can easily confirm from alphaEqn.H.

The second one does not have a meaning from a simulation point of view, as there is only one U in the simulations. You don't keep track of both liquid and gas velocity, as you would do in twoPhaseEulerFoam. However, if you would use indicator functions for that set of equation, you will eventually find U_c=U_l-U_g.

Also, be aware that this is not a counter-gradient term, but more of a convective like term, with the same purpose in the end.