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Exact unsteady Stokes test case

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Old   April 13, 2009, 06:35
Default Exact unsteady Stokes test case
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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
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Old   April 13, 2009, 07:34
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The exact solution is u=0.

Last edited by jugghead; April 13, 2009 at 10:03.
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Old   April 13, 2009, 08:48
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Quote:
Originally Posted by jugghead View Post
The exact solution is u=0.
Is your reply supposed to be funny or haven't you read carefully my post?
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Old   April 13, 2009, 13:32
Default Some exact solutions
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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.
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Old   April 13, 2009, 13:58
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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
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Old   April 13, 2009, 14:15
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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))
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