Convergence issues in extremely low Re problems
 

Hi all! I've been working in a extremely low Reynolds problems, namely Re = 1.16x10^−6. The problem is very simple a 2D water drop in a box filled with petroleum, the parameters are as follows:

rho_w=1000
nu_w=1e-6
rho_p=800
nu_p=3.75e-4
sigma=0.02
g=10
b=600e-6 (box' sides)
dw=100e-6 (water droplets)
dx=10E-6 (structured mesh)

the idea is to predict the sedimentation velocity which is v=3.7x10^-6. (More details and comparisons with other codes here: http://cimec.org.ar/ojs/index.php/mc...view/4648/4580). I've found the following limitations:

1. The curvature calculation procedure is basically useless, the errors in curvature values are greater than 50% (while in Gerris, f.e. they are below 1%). Due to this, I changed the surface tension to sigma=0.00002, since this change doesn't modify the sedimentation velocity but dumps the effect of the surface tension term. Without doing this the parasitic current are so high that the problem cannot be solved.

2. With these new case (low sigma) the solver still has problems, now with convergence, it is extremely difficult to go down in residual values (hundreds of PISO steps due to many outer PIMPLE loops).

3. Even converging to residuals O(1E-13) the final predicted velocity is high respect to the theoretical value, approximately two times.

4. I programmed a interStokesFoam, which doesn't have the convection term div(rho U U) and the velocity prediction was improved, but not at all.

So that, some questions:

a. Why these kind of problem are so hard to solve? I've found that Gerris (Fractional Step p-V coupling) or other codes with monolitic p-V coupling perform really much better (see paper ref)
b. What kind of settings and/or solver changes could improve the quality and speed of the solution (actual setting are similar to damBreak problem but with a lot of PIMPLE, PISO loops and exiting by converge criteria).

Thanks in advance!