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February 17, 2012, 17:26 
test case for navier stokes

#1 
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aaaaaaaaaaaaaa
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Could you tell me which test cases with analytical solution exist for validation or verification of navierstokes equations (compressible flow)?
Also, where will i found the complete setup of them? I know the laminar boundary layer, but due to large computational cost i want another case. Thanks 

February 22, 2012, 17:25 

#2  
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Quote:
for incompressible flow you have several analytical solutions in 2D Poiseuille, couette 

February 23, 2012, 05:09 

#3 
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cfdnewbie
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If you have access to the code and could add a source term, there's an infinite number of analytical solutions for the NS equation with source term.... as far as I know, that's the only method to validate and verifiy your code thoroughly.


February 23, 2012, 06:31 

#4  
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Quote:
An analytical solution for compressible NS equations means you have the functions: u(x,y,z,t) v(x,y,z,t) w(x,y,z,t) p(x,y,z,t) ro(x,y,z,t) T(x,y,z,t) for any x,y,z, and time t. as far as I know it only exists in incompressible 2D poiseuille and couette flows. There is also a 3D incompresible transcient solution. But for sure there is not an infinite number of such solution as you say especially in compressible. If we were able to determine analytical solution of compressible NS equations CFD would certainly not exist any longer !!! If you have these 6 functions for any x,y,z,t then the nobel price is for you my friend !!!! 

February 23, 2012, 06:39 

#5 
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cfdnewbie have you heard about the 7 problems of the millenium proposed by Clay Mathematical Institute?
The analytical solution of NavierStokes equations is the 6th of them !! So if you are able to produce such solution you will also earn 1 million dollars + 1 million dollars of nobel price.. so go ahead you will be rich 

February 23, 2012, 08:06 

#6 
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A_R
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why you don't choose experimental test cases?


February 23, 2012, 10:40 

#7 
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cfdnewbie is referring (I believe) to the method of manufactured solutions for validating the code. That may be your best approach for verifying your code.


February 23, 2012, 11:44 

#8  
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cfdnewbie
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Quote:
So no 1 mio for me, it's just what everybody else in code development is doing ( or should be doing)! 

February 24, 2012, 17:08 

#9 
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By the way, the Clay prize is not for someone providing solutions to the NS equations. It is for someone proving (or disproving) that the 3D incompressible form of the equations has a solution and that it is unique for given initial and boundary conditions + some conditions on the functional spaces all these functions belongs to.
Far more interesting... 

February 25, 2012, 18:25 

#10  
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Filippo Maria Denaro
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Quote:
as far the testcase for compressible flows is concerned, I can suggest to try the compressible Poiselle flow or some particular 1d cases: http://www.waset.org/journals/waset/v43/v4327.pdf http://www.dtic.mil/dtic/tr/fulltext/u2/p010705.pdf 

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