Coner singularity and velocity explosion
 

Hi everyone,

I mostly try to run away from singularities but unfortunately they chase me always.

I am using Volume of Fluid method with several softwares however, the problem is common to all.
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1. One well known singularity that exists is the moving contact line singularity.
That is, when there is a no-slip b.c. on the wall and we advect the meniscus over the wall using the cell face flux, we indirectly consider an implicit slip length equal to half the boundary cell size and move the meniscus.

Example: For a meniscus moving on a wall surface, we never reach mesh independent solution due to the very same reason.
"Finer mesh -> larger singularity -> move away from the real solution".

However Cox and other provide relations considering Navier-Slip length and other parameters such as capillary number. I am considering very low capillary flows so, I can survive with this.

2. Corner singularity: I am looking at a 90 degree junction point (which are the worst regions for numerical simulations) where I specify the contact angle of one of the fluid phases. Considering continuity I can roughly estimate the maximum velocity in the channel. Due to the singularity, I see a velocity approximately 100 times than the real value.
Attached is a figure showing the explosion of velocity vector at these corner cells. The yellow thick line is the interface.

Can anyone guide me if there is a way to avoid this other than changing the 90 degree junction.