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interface curvature in interFoam

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Old   December 14, 2019, 01:55
Default interface curvature in interFoam
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Nguyen Duy Trong
Join Date: Apr 2014
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Hi everyone,


I have a question about interface curvature as below:
Following definition of interface curvature, \kappa is defined as:
\kappa = \nabla\cdot \vec{n}
in which \vec{n} is normal vector of interface that is defined based on volume fraction in each cell as:
\vec{n} = \frac{\nabla \cdot \alpha}{|\nabla \cdot \alpha|}
So:
\vec{n} is volVectorField and then \kappa is volScalarField, is that correct?

However, in interFoam solver, \vec{n} is defined on cell face (\vec{n_f}) as:
\vec{n_f} = \frac{(\nabla \alpha)_f}{|(\nabla \alpha)_f|}
where (\nabla\alpha)_f is defined by interpolation computation as:
(\nabla\alpha)_f = \text{fvc::interpolate}(\nabla\alpha)
then, face unit interface normal flux is defined as:
\hat{n}_f = \vec{n}\cdot S_f

with S_f is the normal vector of cell face (Note that \hat{n}_f then is a surfaceScalarField).

Then, interface curvature is defined as:
\kappa = \nabla\cdot\hat{n}_f

My question is:
- why do we need to interpolate the \nabla\alpha to cell face.
- when we mention about normal vector of interface (interface normal vector) which one is correct \vec{n} defined at cell's center or \vec{n}_f defined at cell's face?
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