2D Flow through parallel planes solution behavior with respect to cell size.

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August 25, 2015, 13:30
2D Flow through parallel planes solution behavior with respect to cell size.
#1
New Member

Pierluigi Morra
Join Date: Apr 2013
Posts: 25
Rep Power: 6
Hello everyone, I picked up the pitzDaily tutorial, changed its geometry in a 2D rectangle, switched off turbulence and tried to simulate the very well known case of an incompressible flow through two parallel planes with a Reynolds equal to 100. The height of the rectangle is 1/15 its length.

I started with a relative coarse grid and plotted the resulting Ux profile along the Y axis. The analytic solution gives a parabola, that is the trend I got from the coarse grid. If I decrease the cell size, the profile starts to flatten, and it gets closer to a case where the Reynolds increases or the viscosity decreases.
I do not understand why.

If you want to reproduced it, I attached it in here. I firstly tried a sampleGrading (150 10 0), then (1200 80 0).
Attached Files
 Flow.zip (13.6 KB, 6 views)

August 25, 2015, 14:16
#2
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Troy Snyder
Join Date: Jul 2009
Location: Akron, OH
Posts: 138
Rep Power: 11
Quote:
 Originally Posted by maCrobo Hello everyone, I picked up the pitzDaily tutorial, changed its geometry in a 2D rectangle, switched off turbulence and tried to simulate the very well known case of an incompressible flow through two parallel planes with a Reynolds equal to 100. The height of the rectangle is 1/15 its length. I started with a relative coarse grid and plotted the resulting Ux profile along the Y axis. The analytic solution gives a parabola, that is the trend I got from the coarse grid. If I decrease the cell size, the profile starts to flatten, and it gets closer to a case where the Reynolds increases or the viscosity decreases. I do not understand why. If you want to reproduced it, I attached it in here. I firstly tried a sampleGrading (150 10 0), then (1200 80 0).
First off, your residual values are rather large. I would suggest decreasing to 1E-5 and 1e-6 for U and p respectively.

 August 25, 2015, 17:06 #3 New Member   Pierluigi Morra Join Date: Apr 2013 Posts: 25 Rep Power: 6 Modifying those values and increasing the number of cells such that SampleGrading (3000 200 0) gives back the same issue. After increasing the maximum number of iterations the solution gets closer to the analytic one again. It is like decreasing cell size makes the code need more iterations to reach convergence. That's counterintuitive to me, why is it so? EDIT: My Answer is that the numerical viscosity helps reaching the parabolic trend quicker because it acts like a stronger force applied to the fluid, then convergence is reached earlier. Last edited by maCrobo; August 26, 2015 at 06:38.

August 26, 2015, 17:06
#4
Senior Member

Troy Snyder
Join Date: Jul 2009
Location: Akron, OH
Posts: 138
Rep Power: 11
First, regarding the residual values, I meant 1e-5 for p and 1E-6 for U.

I believe your issue lies in the the combination of the grid size and the viscosity. Your
grid size is quite large for the viscosity value and the BL will very thin and will require a very
refined near wall grid to resolve.

I changed your velocity from 0.0005 to 0.5 and \nu from 1e-6 to 1e-3 to maintain the
same Reynolds number of 50. Coarse and refined grid velocity profiles near the
inlet and exit are attached.
Attached Images
 coarse.png (11.2 KB, 7 views) refined.png (11.4 KB, 6 views)

 August 27, 2015, 05:39 #5 New Member   Pierluigi Morra Join Date: Apr 2013 Posts: 25 Rep Power: 6 Thanks for the reply. Actually, keeping my constants and changing the tolerance values gave me a nice result.

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