Planar (2D) Poiseuille Flow

Hi take a look at my WebSite, under Computational Reality tutorials number 06 is a viscous fluid flow in 2D with the Navier Stokes constitutive relations.

http://www.lkm.tu-berlin.de/menue/mitarbeiter_sprechstunden/b_emek_abali_msc/

Nice work!!!

Kent

On 18 April 2011 12:51, B. Emek Abali
<email address hidden>wrote:

> Question #152917 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/152917
>
> Status: Open => Answered
>
> B. Emek Abali proposed the following answer:
> Hi take a look at my WebSite, under Computational Reality tutorials
> number 06 is a viscous fluid flow in 2D with the Navier Stokes
> constitutive relations.
>
> http://www.lkm.tu-
> berlin.de/menue/mitarbeiter_sprechstunden/b_emek_abali_msc/
>
> --
> You received this question notification because you are a member of
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you mean FEniCS :) lol

we started a new project based course doing these kind of works with small student groups, all with FEniCS...

Thank you for the information! The tutorials are very helpful. I should join your course lol.

I still do have questions regarding my specific question.

I am considering 2D Poiseuille flow that is two parallel plates of length x=L positioned at y=+H/-H. A pressure gradient is applied that directs the flow and the top and bottom are considered to have no-slip conditions.

So from the Navier-Stokes equation the equation of linear momentum for 2d Poiseuille flow reads:

dp/dx - u(d^2v)/(dy^2) = 0

and

dp/dy = 0

Where:

p=pressure
u=viscosity
v=velocity
x=pipe length
y=pipe width

BCs are such that:

v = 0 at the top and bottom
v inlet = (1-y^2)
p outlet = 0

I guess I am stuck more at the variational formulation of the problem than anything else. I think with the variational formulation part I would be able to solve the problem using FEniCS. I have been reading about the variational formulation through tutorials but I don't understand it completely.

Grazie!

Kyle

Thank yuu again for your help Emek Abali,

I guess the difference is that my problem is steady-state and I would not like it to be time-dependant for now. Do you know what would change in this case?

Kyle

You should drop the partial time derivative parts out of the equation. But remember that You might have numerical problems if the viscosity is not high enough.

On Mon, Apr 18, 2011 at 11:26:25AM -0000, B. Emek Abali wrote:
> Question #152917 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/152917
>
> B. Emek Abali posted a new comment:
> you mean FEniCS :) lol
>
> we started a new project based course doing these kind of works with
> small student groups, all with FEniCS...

Very nice! When we get the new web page in place (working on it), we
should have a page with links to projects/courses that use FEniCS.

I've added a note about your page and will add it once the new pages
are in place. If anyone else knows about related projects/courses that
we should link to, let me know.

--
Anders

I used some handouts in
http://www.tu-chemnitz.de/mathematik/part_dgl/teaching/material/index.en.php

from Roland Herzog (don't know him personally)
http://www.tu-chemnitz.de/mathematik/part_dgl/people/herzog/index.de.php

Thanks B. Emek Abali, that solved my question.