interface curvature in interFoam

ndtrong · December 14, 2019, 01:55

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

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?

einstein_zee · December 16, 2019, 08:36

Hii there,

1. In order to be consistent with FVM, fluxes/forces or ... are calculated over the faces of the computational cell. Also note that surface tension is added as a volumetric force in momentum equation.

2. In general, VOF methods which are not tracking explicitly(by reconstructing the interface) the interface, are not representing the exact shape of the interface. This means you should not worry about which one is correct or not. As far as solution of momentum eq. is concerned the formulation should be done WRT cell faces.

hope this helps...

ndtrong · December 17, 2019, 18:18

Quote:

Originally Posted by einstein_zee

Hii there,

1. In order to be consistent with FVM, fluxes/forces or ... are calculated over the faces of the computational cell. Also note that surface tension is added as a volumetric force in momentum equation.

2. In general, VOF methods which are not tracking explicitly(by reconstructing the interface) the interface, are not representing the exact shape of the interface. This means you should not worry about which one is correct or not. As far as solution of momentum eq. is concerned the formulation should be done WRT cell faces.

hope this helps...

Dear Mr. Hosein

Thank you very much for your comments.
I have another question on comment #2. Could you please make clear on VOF methods which are not tracking explicit, why it does not represent the exact shape of interface? What are their drawback make interface not sharpen?

mAlletto · December 20, 2019, 05:37

the interface is not explicit since it is calculated from the colour function alpha. One disadvantage is that if you consider also surface tension with an implicit formulation of the interface you can generate parasitic currents. A very good article explaining interfoam is this one: https://iopscience.iop.org/article/1.../1/014016/meta

ndtrong · December 22, 2019, 22:49

Dear Michael,

I thank you very much for your comment with related paper.

December 14, 2019, 01:55	interface curvature in interFoam	#1
ndtrong Senior Member Nguyen Duy Trong Join Date: Apr 2014 Posts: 124 Rep Power: 12	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 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? mcfdma likes this.

December 20, 2019, 05:37		#4
mAlletto Senior Member Michael Alletto Join Date: Jun 2018 Location: Bremen Posts: 615 Rep Power: 15	the interface is not explicit since it is calculated from the colour function alpha. One disadvantage is that if you consider also surface tension with an implicit formulation of the interface you can generate parasitic currents. A very good article explaining interfoam is this one: https://iopscience.iop.org/article/1.../1/014016/meta ndtrong likes this.

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December 16, 2019, 08:36		#2
einstein_zee Member Hosein Join Date: Nov 2011 Location: Germany Posts: 93 Rep Power: 14	Hii there, 1. In order to be consistent with FVM, fluxes/forces or ... are calculated over the faces of the computational cell. Also note that surface tension is added as a volumetric force in momentum equation. 2. In general, VOF methods which are not tracking explicitly(by reconstructing the interface) the interface, are not representing the exact shape of the interface. This means you should not worry about which one is correct or not. As far as solution of momentum eq. is concerned the formulation should be done WRT cell faces. hope this helps...

December 22, 2019, 22:49		#5
ndtrong Senior Member Nguyen Duy Trong Join Date: Apr 2014 Posts: 124 Rep Power: 12	Dear Michael, I thank you very much for your comment with related paper.