[Nek5000-users] stokes flow with time-dependent boundary

[nek5000-users at lists.mcs.anl.gov]

On 12/19/2011 06:17 PM, nek5000-users at lists.mcs.anl.gov wrote:
>
> Hi Lailai,
>
> I have used the approach you proposed for solving multiple
> steady stokes problems... you use an artificially large
> timestep.  That works.
>

thank for your reply, if understand correctly, here you are talking 
about the second approach i proposed. For each time step, we solve a 
transient problem with very large internal timestep to quickly get to 
the steady-state solution.
since i am very new to nek5000, thus  i am not sure how to implement 
this method which seems not trivial.

On the other hand, i started from the first example of the Kovasznay 
problem. I remove the time-derivative and convection term by setting the 
density in .rea file to zero, the numerical results agree very well with 
the analytical solution with zero Re number. I guess here the solver is 
just inverting a matrix which seems feasible for a 2D problem but might 
be too expensive or inefficient for a 3D problem.


> If you really have a time-dependent boundary condition, there
> is no reason you can't just use the unsteady Stokes solver
> with whatever timestep is required to accurately resolve your
> temporal bcs.   Note that, in this case, you would indeed have
> the inertial term rho du/dt present in the physics.
>


> Paul
>
>
> On Mon, 19 Dec 2011, nek5000-users at lists.mcs.anl.gov wrote:
>
>> Hello, guys,
>>
>> i am a new guy to Nek5000, i saw the manual of nek5000 that it can 
>> solve the steady stokes flow.
>> i guess when i solve such a flow, do i need to set it as a transient 
>> simulation with time-derivative term included to get  a steady-state 
>> solution? or, i can solve it by a direct solver method to get the 
>> solution immediately?
>>
>> since i want to add some time-dependent boundary condition for the 
>> steady stokes flow, so it will be pretty nice if i can solve it using 
>> the direct solver, for each time step, i solve one stokes flow; if 
>> nek5000 cannot solve it in such a way, i guess i have to use the 
>> first way; then for each time step i have to solve a transient 
>> problem to approach the steady state with some artificial time step 
>> used.
>>
>> i am not sure if i have stated my problem clearly. hopefully you guys 
>> have some experience on the feasibility of the two ways mentioned 
>> above. Thank you in advance.
>>
>> lailai
>>
>>
>>
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