Exact unsteady Stokes test case

neazen · April 13, 2009, 06:35

Hi all,

For stability and accuracy testing purpose I'm looking for an exact unsteady Stokes flow test case. (incompressible with Re = 0)

I've been looking in many papers and books and I wasn't able to find one.

Thanks in advance

jugghead · April 13, 2009, 07:34

The exact solution is u=0.

neazen · April 13, 2009, 08:48

Quote:

Originally Posted by jugghead

The exact solution is u=0.

Is your reply supposed to be funny or haven't you read carefully my post?

Jonas Holdeman · April 13, 2009, 13:32

Refer to Gresho & Sani, Incompressible Flow and the Finite Element Method (1998), section 3.16.1d, p660. These are 2D Taylor vortex solutions and generalizations. They have periodic boundary conditions and decay exponentially from their initial condition. Not very interesting or challenging (basically they are eigenfunctions of the Laplacian operator).

More interesting behaviors are limited to 1D.

neazen · April 13, 2009, 13:58

Thanks for the reference (those having the two volumes edition should look at page 750).

I'll try to derive a Stokes flow test case from it (with nu=1 and a forcing function) and see how it will look

neazen · April 13, 2009, 14:15

For those interested I also found this test case:

Code:

u = sin(x)sin(y+t)
v = cos(x)cos(y+t)
p = cos(x)sin(y+t)
with:
fx = sin(x)(cos(y+t) + sin(y+t))
fy = cos(x)(3cos(y+t) - sin(y+t))

April 13, 2009, 06:35	Exact unsteady Stokes test case	#1
neazen New Member Join Date: Apr 2009 Posts: 8 Rep Power: 17	Hi all, For stability and accuracy testing purpose I'm looking for an exact unsteady Stokes flow test case. (incompressible with Re = 0) I've been looking in many papers and books and I wasn't able to find one. Thanks in advance

April 13, 2009, 07:34		#2
jugghead New Member Join Date: Mar 2009 Posts: 27 Rep Power: 17	The exact solution is u=0. Last edited by jugghead; April 13, 2009 at 10:03.

April 13, 2009, 13:32	Some exact solutions	#4
Jonas Holdeman Senior Member Jonas T. Holdeman, Jr. Join Date: Mar 2009 Location: Knoxville, Tennessee Posts: 128 Rep Power: 18	Refer to Gresho & Sani, Incompressible Flow and the Finite Element Method (1998), section 3.16.1d, p660. These are 2D Taylor vortex solutions and generalizations. They have periodic boundary conditions and decay exponentially from their initial condition. Not very interesting or challenging (basically they are eigenfunctions of the Laplacian operator). More interesting behaviors are limited to 1D.

April 13, 2009, 13:58		#5
neazen New Member Join Date: Apr 2009 Posts: 8 Rep Power: 17	Thanks for the reference (those having the two volumes edition should look at page 750). I'll try to derive a Stokes flow test case from it (with nu=1 and a forcing function) and see how it will look __________________ If a problem can be solved, there is nothing to worry about. If it can't be solved, worrying will do no good. So be Zen and stay Zen

April 13, 2009, 14:15		#6
neazen New Member Join Date: Apr 2009 Posts: 8 Rep Power: 17	For those interested I also found this test case: Code: u = sin(x)sin(y+t) v = cos(x)cos(y+t) p = cos(x)sin(y+t) with: fx = sin(x)(cos(y+t) + sin(y+t)) fy = cos(x)(3cos(y+t) - sin(y+t)) __________________ If a problem can be solved, there is nothing to worry about. If it can't be solved, worrying will do no good. So be Zen and stay Zen

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