[petsc-users] ex42 question

[Matthew Knepley]

On Wed, Apr 16, 2014 at 4:48 PM, Sang pham van <pvsang002 at gmail.com> wrote:

> Hi Jed,
>
> I modified the ex43 code to enforce no-slip BCs on all boundaries.
> I run the code with volume force (0,-1) and isoviscosity. The expected
> result is Vx = Vy = 0 everywhere, and linearly decreasing pressure (from to
> to bottom).
> In the attached is plot of velocity field and pressure, so there is still
> a (light) flow in middle of the domain. Do you know why the solution is
> that, and what should I do to get the expected result?
>

It sounds like it is due to discretization error. Your incompressibility
constraint is not verified element-wise
(I think ex43 is penalized Q1-Q1), so you can have some flow here. Refine
it and see if it converges toward
0 flow.

   Matt


> Thank you.
>
> Sang
>
>
>
>
> On Wed, Mar 26, 2014 at 2:38 PM, Jed Brown <jed at jedbrown.org> wrote:
>
>> Sang pham van <pvsang002 at gmail.com> writes:
>>
>> > Hi Dave,
>> > I guess you are the one contributed the ex42 in KSP's examples. I want
>> to
>> > modify the example to solve for stokes flow driven by volume force in 3D
>> > duct. Please help me to understand the code by answering the following
>> > questions:
>> >
>> > 1. Firstly, just for confirmation, the equations you're solving are:
>> >      \nu * \nabla \cdot \nabla U - \nabla P = 0 and
>>
>> For variable viscosity, it must be formulated as in the example:
>>
>>   \nabla\cdot (\nu D U) - \nabla P = 0
>>
>>   where  D U = (\nabla U + (\nabla U)^T)/2
>>
>> >      \nabla \cdot U = 0
>> >
>> >       where U = (Ux,Uy,Uz), \nu is variable viscosity?
>> >
>> >  2. Are U and P defined at all nodes? (I googled the Q1Q1 element, it
>> looks
>> > like a box element with U and P defined at 8 corners).
>>
>> Yes.
>>
>> >  3. Are nodes' coordinate defined though the DA coordinates?
>>
>> Yes, though they are set to be uniform.
>>
>> >  4. How can I enforce noslip BC, and where should I plug in volume
>> force?
>>
>> Enforce the Dirichlet condition for the entire node.
>>
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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