Spurious velocity issue in hybrid version of interFoam and interface tracking method

mykkujinu2201 · July 30, 2021, 01:51

Dear Forum,

Currently, I am preparing hybrid version of VOF (interFoam) and interface tracking method to prevent spurious velocity issue.
VOF will calculate pressure, velocity and marker while interface tracking method will calculate capillary force.
I referenced the paper of Mosayeb Shams. (Shams, M., Raeini, A. Q., Blunt, M. J. & Bijeljic, B. A numerical model of two-phase flow at the micro-scale using the volume-of-fluid method. Journal of Computational Physics 357, 159–182 (2018).
)
He made the code (CLSF, contour-level surface force method) in OpenFOAM and the base solver is interFoam.
Isocontour of marker is reconstructed to obatain interface elements.
According to Shams, intereface elements are constructed based on faces of fixed grid where sharpen marker changes rapidly.
Thus, each element has its corresponding face and they are called 'mixed face'.
After obtaining interface elements, capillary force is directly calculated for each element.
Finally the result will be interpolated back to mixed face to calculate flux due to capillary force.

I made the code and now I am validating it.
The validation cases are 2D and 3D static bubble simulations.
For 2D cases, spurious velocity is reduced below 10^(-10) m/s and it predicted pressure well. (Results of time series of max. spurious velocity and pressure along the centerline are attached.)

However, when I tested for 3D cases, the flow field does not converge showing spurious velocity issue.
I can not figure out the reason or the solution yet.

I tested 3D case in both serial and parallel run but results are same so I think this is not due to parallel computing part.
I exported control points of interface elements to compare.
However, the control points are well reconstructed.
In addition, if control points are not tracked well, same issue should come for 2D tests.

Does anyone had similar issue or any opinion?

Best,
Jun

mykkujinu2201 · August 4, 2021, 04:50

Dear Forums,

I tested for different sizes of grid.

For 16 by 16 by 16 or 8 by 8 by 8, the code runs and reduces maximum spurious velocity to the order of $10^{-10}$ [m/s].

For the finer grid (32 by 32 by 32), it reduces the maximum spurious velocity to the order of $10^{-3}$ [m/s].
However, it does not decreases more than the limit.
In addition, even though the boundary conditions and the shape are symmetric, the flow gets asymmetric behaviour.

It seems that the reconstruction of the interface and the calculation of capillary force at each interface element works fine but the interpolating back to the "mixed faces" has a problem. Also, the problem is dependent on the mesh size. I followed the interpolating method given in Shams' paper in the previous post.

Do you have any opinions or comments about it?

Best,
Jun

randolph · August 7, 2021, 20:03

Jun,

Is your VOF solver well-balanced?

Thanks,
Rdf

mykkujinu2201 · August 8, 2021, 10:36

Dear Randolph,

First of all, thank you so much for the reply.

As far as I know, the reconstructed interface is used to compute capillary force at the center of mixed faces, and it is well-balanced.

The capillary flux is given as below.

$\phi_\textrm{cap.}=(\vec{f}_\textrm{cap.}\cdot\frac{\nabla \alpha_S}{\lvert \nabla \alpha_S \rvert})\nabla_f \alpha_C$ ,
where $\phi_\textrm{cap.},$ , $\vec{f}_\textrm{cap.}$ , $\alpha_S$ , $\nabla_f \alpha_C$ are caipllary flux, capillary force, smoothed marker, surface normal graident (snGrad) of sharpened marker, respectively.

Mosayeb Shams also said that this gives a balanced-force algorithm in his paper.

I checked my code several times from the start to the end.

Interface elements are well reconstructed and the capillary force is directly calculated from the interface.

I doubt about forcing term itself, however, I do not know the reason.

I found that until 17 by 17 by 17, spurious velocity reduces very well.

From 18 by 18 by 18, the issue starts.

As you pointed out, maybe this is not well-balanced.

However, I do not know whether it is really well-balanced or not.

Would you mind if I ask you whether the equation above is well-balanced or not?

Best regards,
Jun

randolph · August 8, 2021, 19:39

Jun,

The equation does not really tell much about whether a numerical scheme is well-balanced or not. The well-balanced property does not really mean whole a lot for PDE, it referring to the numerical scheme. After the equation is discretized into matrix form, if no special care is taken, the well-balanced property is typically not enured.

I am no expert in well-balanced numerical schemes. But from what I know, a robust well-balanced scheme is tricky. Why not drop the guy in the JCP paper an email with your question?

Thanks,
Rdf

suchi89 · July 19, 2022, 17:39

Modeling bubbles as 2D might be the source of the issue. You see, these are essentially very three dimensional in nature and that might be your source of error.

Also, I have worked on similar problem to reduce spurious currents in these types of multiphase phenomena. We were able to validate with a number of different applications. Might be of assistance to you. https://asmedigitalcollection.asme.o...olume-of-Fluid

August 4, 2021, 04:50	Still same problem exitst	#2
mykkujinu2201 Member Jun Join Date: Nov 2015 Posts: 57 Rep Power: 11	Dear Forums, I tested for different sizes of grid. For 16 by 16 by 16 or 8 by 8 by 8, the code runs and reduces maximum spurious velocity to the order of $10^{-10}$ [m/s]. For the finer grid (32 by 32 by 32), it reduces the maximum spurious velocity to the order of $10^{-3}$ [m/s]. However, it does not decreases more than the limit. In addition, even though the boundary conditions and the shape are symmetric, the flow gets asymmetric behaviour. It seems that the reconstruction of the interface and the calculation of capillary force at each interface element works fine but the interpolating back to the "mixed faces" has a problem. Also, the problem is dependent on the mesh size. I followed the interpolating method given in Shams' paper in the previous post. Do you have any opinions or comments about it? Best, Jun

July 19, 2022, 17:39	Not sure if you can model bubbles as 2D?	#6
suchi89 New Member Join Date: Apr 2012 Posts: 4 Rep Power: 14	Modeling bubbles as 2D might be the source of the issue. You see, these are essentially very three dimensional in nature and that might be your source of error. Also, I have worked on similar problem to reduce spurious currents in these types of multiphase phenomena. We were able to validate with a number of different applications. Might be of assistance to you. https://asmedigitalcollection.asme.o...olume-of-Fluid

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August 7, 2021, 20:03		#3
randolph Senior Member Reviewer #2 Join Date: Jul 2015 Location: Knoxville, TN Posts: 141 Rep Power: 11	Jun, Is your VOF solver well-balanced? Thanks, Rdf

August 8, 2021, 10:36		#4
mykkujinu2201 Member Jun Join Date: Nov 2015 Posts: 57 Rep Power: 11	Dear Randolph, First of all, thank you so much for the reply. As far as I know, the reconstructed interface is used to compute capillary force at the center of mixed faces, and it is well-balanced. The capillary flux is given as below. $\phi_\textrm{cap.}=(\vec{f}_\textrm{cap.}\cdot\frac{\nabla \alpha_S}{\lvert \nabla \alpha_S \rvert})\nabla_f \alpha_C$ , where $\phi_\textrm{cap.},$ , $\vec{f}_\textrm{cap.}$ , $\alpha_S$ , $\nabla_f \alpha_C$ are caipllary flux, capillary force, smoothed marker, surface normal graident (snGrad) of sharpened marker, respectively. Mosayeb Shams also said that this gives a balanced-force algorithm in his paper. I checked my code several times from the start to the end. Interface elements are well reconstructed and the capillary force is directly calculated from the interface. I doubt about forcing term itself, however, I do not know the reason. I found that until 17 by 17 by 17, spurious velocity reduces very well. From 18 by 18 by 18, the issue starts. As you pointed out, maybe this is not well-balanced. However, I do not know whether it is really well-balanced or not. Would you mind if I ask you whether the equation above is well-balanced or not? Best regards, Jun

August 8, 2021, 19:39		#5
randolph Senior Member Reviewer #2 Join Date: Jul 2015 Location: Knoxville, TN Posts: 141 Rep Power: 11	Jun, The equation does not really tell much about whether a numerical scheme is well-balanced or not. The well-balanced property does not really mean whole a lot for PDE, it referring to the numerical scheme. After the equation is discretized into matrix form, if no special care is taken, the well-balanced property is typically not enured. I am no expert in well-balanced numerical schemes. But from what I know, a robust well-balanced scheme is tricky. Why not drop the guy in the JCP paper an email with your question? Thanks, Rdf