# test case for navier stokes

 User Name Remember Me Password
 Register Blogs Members List Search Today's Posts Mark Forums Read

 LinkBack Thread Tools Display Modes
 February 17, 2012, 17:26 test case for navier stokes #1 New Member   aaaaaaaaaaaaaa Join Date: Apr 2011 Posts: 23 Rep Power: 8 Could you tell me which test cases with analytical solution exist for validation or verification of navier-stokes 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
Senior Member

Join Date: Aug 2011
Posts: 271
Rep Power: 9
Quote:
 Originally Posted by panou Could you tell me which test cases with analytical solution exist for validation or verification of navier-stokes equations (compressible flow)? Thanks
Up to my knowledge there is no analytical solution of compressible NS equations, but try this: http://www.springerlink.com/content/khk855n125555p7r/

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

 February 23, 2012, 05:09 #3 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 13 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
Senior Member

Join Date: Aug 2011
Posts: 271
Rep Power: 9
Quote:
 Originally Posted by cfdnewbie 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.
Hi cfdnewbie,

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 Senior Member   Join Date: Aug 2011 Posts: 271 Rep Power: 9 cfdnewbie have you heard about the 7 problems of the millenium proposed by Clay Mathematical Institute? The analytical solution of Navier-Stokes 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 Senior Member     A_R Join Date: Jun 2009 Posts: 120 Rep Power: 10 why you don't choose experimental test cases?

 February 23, 2012, 10:40 #7 Senior Member   Join Date: Jul 2009 Posts: 247 Rep Power: 12 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
Senior Member

cfdnewbie
Join Date: Mar 2010
Posts: 557
Rep Power: 13
Quote:
 Originally Posted by agd 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.
Yes, thank you, I am indeed. It's the standard method used widely for code verification, and the emphasis is on Navier Stokes WITH source term, as mentioned in my first post. I wouldnt trust a code not verified that way with a rigorous test suite.

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 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 797 Blog Entries: 17 Rep Power: 21 By the way, the Clay prize is not for someone providing solutions to the N-S 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... FMDenaro likes this.

February 25, 2012, 18:25
#10
Senior Member

Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,641
Rep Power: 41
Quote:
 Originally Posted by sbaffini By the way, the Clay prize is not for someone providing solutions to the N-S 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...
that's right, exact particular solutions of NS exist ...

as far the test-case 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/v43-27.pdf
http://www.dtic.mil/dtic/tr/fulltext/u2/p010705.pdf

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post steph79 OpenFOAM Pre-Processing 4 August 3, 2010 07:45 adona058 OpenFOAM Running, Solving & CFD 3 May 3, 2010 18:46 venkatesh4386@gmail.com FLUENT 0 March 9, 2009 13:04 Alex FLUENT 0 April 9, 2006 08:23 Eric Lenormand Main CFD Forum 0 March 2, 2000 07:54

All times are GMT -4. The time now is 10:45.

 Contact Us - CFD Online - Privacy Statement - Top