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Accuracy problem of HO schemes on unstructured mesh, HO scheme gives 1st order result 

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December 24, 2011, 13:21 
Accuracy problem of HO schemes on unstructured mesh, HO scheme gives 1st order result

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Hi,
I am trying to develop an unstructured finite volume solver and it has problem with solution accuracy. Here the details;  The test problem is standard lid driven cavity flow at Re = 1000.  Colocated arrangement is used with MIM  MESH is triangular and about 2000 cells  The convective terms are discretized using 1st order upwind FOU or MUSCL scheme  SIMPLE algorithm is used The point I am stuck is that; when I select FOU scheme, my solver gives exactly the same result that is obtained from using a commercial solver using the same mesh. However, I cannot obtain the same agreement when I used MUSCL scheme. The difference between my solver result and that of commercial is very big. Actually my solver give nearly the same result when FOU scheme is used. I tried several different HO formulations, ie. TVD , NVSF , GAMMA scheme, but my solution accuracy did not changed from first order. Any help with this would be greatly appreciated. Thanks in advance. 

December 24, 2011, 14:36 

#2 
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Hi gemini,
did you test the convergence of your formulation beforehand? Does it give second order for a convergence test? Cheers 

December 24, 2011, 16:21 

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hi,
I could not get the point what you meant. could you give me more specific examples. both FOU and HO SCHEME implementation of my code converges well and i did not observe any convergence difficulty. on the other hand, is there any critical issues in FV discretization on unstructured meshes? I have used overrelaxed approach and MIM (majumdar formulation) in my code and as I point before the results with FOU scheme match closely with literature results. 

December 24, 2011, 16:31 

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Hello, I will try to make more clear what I meant.
If you write your own code, it is customary to test the code with an analytical example before starting to do "real" computations. For example, for linear scalar advection, you could use a simple transport to test your scheme. For Euler or NavierStokes, the transport of a density profile gives you a first clue if something is wrong. The basic idea is to test your implementation with examples for which you know the solution, so you can be sure that your code itself is ok. If you need more help, let me know! read e.g.: http://www.innovativecfd.com/manufa...overview.html http://csm.mech.utah.edu/content/201...ationtesting/ http://www.personal.psu.edu/jhm/ME54...MS_summary.pdf cheers 

December 24, 2011, 18:47 

#5  
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Arjun
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Quote:
Your implementation may have some problem. In all the higher order scheme implementation, a normalized variable at the face is calculated. Based on this variable it is decided that whether to use higher order scheme or just use first order upwind scheme. In your case it seems the normalized variable at face that you calculate is such that always FOU is selected. So check your implementation. 

December 24, 2011, 19:14 

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Quote:
cheers! 

December 24, 2011, 19:25 

#7  
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Yes you can, but it does not say that everyone else is doing what you are doing. 

December 24, 2011, 19:34 

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So how come you assumed that he had such a switch implemented, and how come you stated that all codes had such a switch? Am I the one making assumptions and invalid generalizations here, or is it you, my friend? )
Maybe we should stop this cat fight and try to help the guy asking his question! ) Cheers! Last edited by cfdnewbie; December 24, 2011 at 20:28. Reason: Better sense! 

December 24, 2011, 21:01 

#9  
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I have already answered him and to him it will make sense. It is clear that you do not have much experience implementing the schemes he was talking about. Spend some time with this page: http://www.cfdonline.com/Wiki/Discr...onvection_term 

December 24, 2011, 21:37 

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December 25, 2011, 03:22 

#11 
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duri
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Gemini, check you limiter implementation, I think it some how pushes to first order reconstruction at face.


December 26, 2011, 05:45 

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I found the mistake, it is indeed a simple mistake of implementation of flux direction check. flow direction check must be performed using face normal velocities (or simply normal mass flux) not V_x for xmomentum and V_y for ymomentum Thanks to everybody Last edited by gemini; December 26, 2011 at 07:28. Reason: problem solved. 

December 27, 2011, 22:01 

#13  
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Quote:
glad it worked out for you. Generally it is a silly mistake that creates problems. 

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