# Solution at high reynolds numbers

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 October 18, 2013, 02:54 Solution at high reynolds numbers #1 New Member   Join Date: Jan 2013 Posts: 17 Rep Power: 4 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

 October 18, 2013, 12:48 #2 Member   Reza Join Date: Mar 2009 Location: Appleton, WI Posts: 99 Rep Power: 8 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 and kamyar like this.

 October 18, 2013, 13:30 #3 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 1,659 Rep Power: 23 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. Please, give us more details kamyar likes this.

 October 18, 2013, 14:06 #4 New Member   Join Date: Jan 2013 Posts: 17 Rep Power: 4 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?

October 18, 2013, 14:12
#5
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Filippo Maria Denaro
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Quote:
 Originally Posted by kamyar 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?

 October 18, 2013, 14:24 #6 New Member   Join Date: Jan 2013 Posts: 17 Rep Power: 4 I forgot to say I'm solving the Incompressible steady state flow equations.

October 18, 2013, 14:31
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Filippo Maria Denaro
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Quote:
 Originally Posted by kamyar 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

 October 18, 2013, 14:40 #8 New Member   Nic T Join Date: Oct 2013 Posts: 2 Rep Power: 0 What kind of up-winding are you using?

 October 18, 2013, 14:59 #9 New Member   Join Date: Jan 2013 Posts: 17 Rep Power: 4 I've used both first and second order upwind scheme. It has been described in versteeg.

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