[Nek5000-users] Infinite Prandtlnumber with Nek5000

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

Hello, Jan,

We have in fact solved a similar problem as you face now. In our case, 
we have steady Stokes equation at each time step,
in the absence of time derivative and convection term. However we have 
time-dependent volume forcing and boundary
conditions, as we solve for fluid-structure interactions in the Stokes 
regime.

You only need to change the source code for one thing. By changing the 
flags in the .rea file, you can easily turn
off the two terms. However, the code only runs for 1 time step even if 
you specify for example 10 total time steps, which makes sense
as NEK realizes this is a steady problem. NEK5000 does not see that the 
next time step, BCs and forcing will be changed, and so
as the flow.

So I remember I only commented two lines of the source code to achieve 
this, in the file 'connect2.f', subroutine 'rdparam',
this is what I have done (i am using a quite old version of the NEK, so...)

       IF (.NOT.IFTRAN) THEN
c         PARAM(11) = 1.0 !lailai comment for steady stokes
c         PARAM(12) = 1.0 !lailai comment for steady stokes
          PARAM(19) = 0.0
       ENDIF

Of course you need to set the flags right in .rea file, which you can 
find the details on the webpage. You also need to
solve for heat equations to get T. Then in the userchk subroutine, you 
calculate the T-dependent buoyancy forcing at each time step.
Solve the flow with new forcing terms. This should be all manageable.

cheers and good luck,

lailai



On 2015/8/5 12:15, nek5000-users at lists.mcs.anl.gov wrote:
> Hi all,
> I was wondering if it is possible to use Nek5000 for simulations in 
> the infinite Prandtlnumber regime (e.g. planetary mantles). This would 
> require to solve the NS Stokes equation without the time derivative 
> and advection term and the heat equation for T:
>
> 1) Solve visc * laplace u - grad p + buoyancy = 0 and div u = 0, where 
> bouyancy depends on a given T field and a Rayleigh number
> 2) Update T by solving dT/dt + u grad T = diff * laplace T (+ other 
> sources)
> 3) go back to 1 with the new T field, repeat
>
> More realistic models would then use a varying viscosity.
> I looked at the steady state example (kov_st_state), but this is 
> missing the time depencence via the Temperature. Any hints on the 
> possibility would be much appreciated.
>
> Thanks,
> Jan
>
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-- 
Lailai Zhu
Laboratory of Fluid Mechanics and Instabilities LFMI
EPFL STI IGM LFMI ME A2 408 (Bâtiment ME) Station 9
CH-1015 Lausanne Switzerland