Divergence of u*Phi in conservative form.
Dot product of u with gradient of Phi in non-conservative form.
Dear Sir,
I didn't get why this happens.
In the below pictures, one can see how the equation changes.
In conservative equation, divergence of (u * PHI) is from non-conservative term. (u.grad(PHI) )
It's the volume fraction. Simply the level set variable. One in inner phase and 0 in outer phase.
Dear Shaksham,
In the continuous realm, both approaches are exactly equivalent, provided that continuity is satisfied simultaneously. It is in discretizations that differences arise. As far as I know, COMSOL uses a finite element approach. Thus the approximation is enforced by making zero weighted residuals in weak form, that is, the degree of continuity that is required from the approximate solutions is lower than that of the original equations. When the conservation equations are written in conservative form, the volume integral of the Div .(u phi) becomes a surface integral of n . (u phi) where n is the normal to the boundaries. Thus you have to consider these boundary contributions, which may be exploited via natural boundary conditions. I hope this helps.
Juan
Dear Sir,
As
\nabla\cdot(\varphi \mathbf{F}) = (\nabla\varphi) \cdot \mathbf{F} + \varphi \;(\nabla\cdot\mathbf{F}).
You can see in 2 pics posted in comments above, LHS is used in conservative form and first term of RHS in non-conservative form. According to you, only discretisation changes, but not the basic equation. It means, the equations written in both cases are actually the same (because div. of U is zero, the second term of RHS).
Thanks to you Sir.
It is established now that equation are more or less the same, only the code changes, which I haven't started till now.
Saksham Sharma
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