# Poisson convergence for 2D microfluidic duct

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May 19, 2012, 12:44
Poisson convergence for 2D microfluidic duct
#1
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Tristan
Join Date: Apr 2012
Posts: 5
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I'm trying to simulate a 2D microfluidic channel flow using the projection method with a Poisson pressure correction solver in Fortran (code attached should be renamed with .f90 extension).

I've used the code successfully for larger-scale geometry with different flow conditions, but I can't seem to get the Poisson solver to converge for the microfluidic flow used.

If anyone feels ambitious, I'd appreciate some pointers.
Attached Files
 T1_v2.txt (25.9 KB, 9 views)

May 19, 2012, 17:50
#2
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Arjun
Join Date: Mar 2009
Location: Nurenberg, Germany
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Quote:
 Originally Posted by twolfe13 If anyone feels ambitious, I'd appreciate some pointers.

There is nothing special, Poisson problems are solved by people across the globe all the time.

As far as your case is concerned, it seems you are using cartesian grid with uniform spacing. In this case you can use FFT based solver or Block tri diagonal method (use Fishpack). Both of them are very fast direct solvers so there is no question of not converging.

Good luck.

May 19, 2012, 18:09
#3
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Tristan
Join Date: Apr 2012
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Quote:
 Originally Posted by arjun As far as your case is concerned, it seems you are using cartesian grid with uniform spacing. In this case you can use FFT based solver or Block tri diagonal method (use Fishpack). Both of them are very fast direct solvers so there is no question of not converging.

Actually, I'm using a staggered mesh with points clustered on the upper and lower wall boundaries and the left inlet boundary. I'm currently using a Gauss-Seidel method to solve the Poisson equation with successive over relaxation (SOR).

As I mentioned before, the solution was converging before changing the scale and fluid properties.

May 19, 2012, 19:22
#4
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Arjun
Join Date: Mar 2009
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Quote:
 Originally Posted by twolfe13 Thanks for your reply! Actually, I'm using a staggered mesh with points clustered on the upper and lower wall boundaries and the left inlet boundary. I'm currently using a Gauss-Seidel method to solve the Poisson equation with successive over relaxation (SOR). As I mentioned before, the solution was converging before changing the scale and fluid properties.

you should realize that solution convergence and Poisson problem convergence are two separate issues.

Poisson problem convergence is condition by which you get solution convergence, but it is no guarantee.

Further I guess mostly Poisson problem is needed for pressure equation which I assume are the points at cell centers and not on the velocity locations of segregated system.

Lately there has been lots of such questions about convergence. When people try to write their code and quickly find that code works for simple cases but has a problem with difficult or large cases. The issue is that code's correctness is no guarantee for convergence. Commerical solvers have to play lots of tricks to keep solver convergent.

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