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neazen April 13, 2009 06:35

Exact unsteady Stokes test case
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


Originally Posted by jugghead (Post 212694)
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

Some exact solutions
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:


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

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