[Nek5000-users] [*] Re: [*] Re: RB convection with high Rayleigh numbers

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

Hi Mani,

Note that your other email did not go to the users list because
of the size of the attachments.  I got it though and tried it.

It looks like the following steps should work ---

    .reduce COURANT to 2.0 instead of 5.0
    .set TORDER=2
    .set initial DT (param 12) to .001
    .reduce lx1 to 5  and lxd to 8 in your SIZE file


I tried this and it seems to work ok, save that I ran my
case w/ Pr=1  (param 2).

Your case w/ p2=6.8 is a bit harder, so you may need to also
use the reduced initial Ra values per your .usr file.

Once you are at the target Ra, you can increase lx1, lxd, and
Torder, then restart.


The issue with the walls is that they trap the fluid in the
corner.  Then when the heating is turned on you get a 
stagnant hot spot that builds up until it finally goes 
unstable --- this happens on a timescale faster than the
early-time convective timescale (which is relatively long
until the flow really starts moving), so the explicit
treatment of the buoyancy leads to an instability.

Reducing Courant to 2.0 instead of 5.0 forces nek5000 to
reduce dt more severely.   Note that we're able to exceed
CFL of unity for convection because of the OIFS convective
time integrator.   The explicit Boussinesq forcing, however,
has it's own timestep restriction and tends to dominate the
stability constraints at early times until the flow is moving.

Paul





On Sun, 16 May 2010, nek5000-users at lists.mcs.anl.gov wrote:

> Hi Paul,
>
>    Thank you for your time on this problem. The geometry is a 2D box with 
> no-slip velocity boundary conditions on all sides and the temperature 
> boundary conditions are insulating on the side walls and the usual fixed 
> temperatures on the top and bottom walls. I will try out your code 
> immediately.
>
> Regards,
> Mani chandra
> On 05/16/2010 09:14 AM, nek5000-users at lists.mcs.anl.gov wrote:
>> 
>> Hi Mani,
>> 
>> I've added an example of a case that should run out to Ra=10^8
>> in the /benard directory of the repo (high_ray.blah is the case).
>> 
>> I've run this with lx1=5, lxd=9 and it will get to Ra=10^8.
>> (In reality, I ran tests with 4 separate runs, 10^k, k=5,6,7,8. I then a 
>> created "high_ray.usr" file that would march through this sequence in a 
>> single run...)
>> 
>> Once you establish the flow at the desired Ra, you can then
>> bump lx1 to say 7 or 8 --- that should be sufficient for Ra=10^8
>> I think.  Even lx1=5 is looking pretty good with the given mesh.
>> 
>> 
>> Also, you can reduce the CFL in the .rea file and increase Torder
>> to 3, so that you will increase your temporal accuracy.
>> 
>> I initially set the parameters so that it would march quickly
>> to Ra=10^8.
>> 
>> The high-Ra test case uses periodic bcs and a uniform mesh in X.
>> If you want vertical walls then you should likely use a nonuniform
>> mesh in X.   The "high_ray.box" file shows how the nonuniform mesh in Y is 
>> created.  A similar set up could be used for nonuniformity
>> in both X and Y.
>> 
>> 
>> Paul
>> 
>> 
>> 
>> On Sun, 16 May 2010, nek5000-users at lists.mcs.anl.gov wrote:
>> 
>>> Hi Paul,
>>>
>>>    Thanks for the reply. I have a doubt whether one should increase the 
>>> polynomial order or the number of elements with a fixed order for this 
>>> case. As I understand from your illustration of the rotating cone case, 
>>> increasing the polynomial order leads to a much better solution than with 
>>> the same number of points generated using more elements with a lower order 
>>> polynomial.
>>> 
>>> Also how do I use the fast tensor-product solver? Is there some flag that 
>>> I need to turn on?
>>> 
>>> Regards,
>>> Mani chandra
>>> On 05/15/2010 09:05 PM, nek5000-users at lists.mcs.anl.gov wrote:
>>>> 
>>>> Hi Mani,
>>>> 
>>>> I've not tried to go this high yet, but there are several std
>>>> techniques to pushing the envelope.
>>>> 
>>>> First, you should try to get an estimate of your expected resolution
>>>> requirements at the target Ra.   Then, guess that you might want to
>>>> run that simulation at say, lx1=10 or 12; and build the corresponding
>>>> mesh (number of elements in x and y); but start the compuation at
>>>> much lower Ra, with lx1=4, say.
>>>> 
>>>> Then work your way up in Ra, say by a factor of 10 in each successive
>>>> run, while also increasing lx1 as needed.
>>>> 
>>>> Note that for the flow in a box, you might find it faster to use
>>>> the fast tensor-product solver for the pressure, if using the Pn-Pn-2
>>>> method --- this is not always the case, but for some very difficult
>>>> problems (e.g., highly refined meshes), it does work better.
>>>> 
>>>> Paul
>>>> 
>>>> 
>>>> On Sat, 15 May 2010, nek5000-users at lists.mcs.anl.gov wrote:
>>>> 
>>>>> Hi,
>>>>>
>>>>>    I'm trying to simulate RB convection in a 2D box of aspect ratio 2:1. 
>>>>> I'd like to simulate cases with Rayleigh numbers of the order of 10^7 - 
>>>>> 10^8. But I'm barely able to do 10^5 and that too with a time step of 
>>>>> 10^-6. For the mesh I took 8 spectral elements in the x direction and 4 
>>>>> spectral elements in the y direction with 48 points within each of them. 
>>>>> Is there any way one can reach higher Ra numbers?
>>>>> 
>>>>> Regards,
>>>>> Mani chandra
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