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 kamyar October 18, 2013 02:54

Solution at high reynolds numbers

Hi
I've written a code for solving the Navier Stokes equation using element based finite volume method on a co-located grid.
My problem is that the code works fine when the Reynolds number isn't too high. but when i increase the Reynolds number the code diverges. I've tried to run the code on different problems ( Cavity and flow between two plates) and on all of them i couldn't get any results at high Reynolds numbers.
Does anybody know what the problem could be? It would be great if someone could help me.
thank you

 triple_r October 18, 2013 12:48

Are you using any kind of up-winding? Your numerical method might be unstable when Peclet number is high for the elements. Also, do these problems come up when the flow is turbulent? or is the Reynolds number not high enough for turbulence?

 FMDenaro October 18, 2013 13:30

This behavior is typical for some formulations, for example centred discretization in FD and FV methods or spectral methods without de-aliasing or FE without stabilization.
At first, try refining the grid in such a way to estimate a cell Reynolds number no greater than 2. It is stable?
If you are solving turbulence, then you are encountering problem typical of unresolved DNS with non-stabilized method.

 kamyar October 18, 2013 14:06

The flow is laminar and I'm using the first and second order upwind scheme.
For the cavity problem I could get results for Reynolds number of 1000 but I'm struggling to get results for Reynolds number of 3200. In the case of wavy channel I couldn't get any results for Reynolds number higher than 75.
How can i improve my upwind scheme?

 FMDenaro October 18, 2013 14:12

Quote:
 Originally Posted by kamyar (Post 457712) The flow is laminar and I'm using the first and second order upwind scheme. For the cavity problem I could get results for Reynolds number of 1000 but I'm struggling to get results for Reynolds number of 3200. In the case of wavy channel I couldn't get any results for Reynolds number higher than 75. How can i improve my upwind scheme?
what about the cfl number you are using?

 kamyar October 18, 2013 14:24

I forgot to say I'm solving the Incompressible steady state flow equations.

 FMDenaro October 18, 2013 14:31

Quote:
 Originally Posted by kamyar (Post 457716) I forgot to say I'm solving the Incompressible steady state flow equations.

ok, consider also that the 2D lid-driven cavity flow starts to become unsteady after Re=1000. I think you should run an unsteady formulation

 No Body Cares October 18, 2013 14:40

What kind of up-winding are you using?

 kamyar October 18, 2013 14:59

I've used both first and second order upwind scheme. It has been described in versteeg.

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