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

Sun May 16 10:35:19 CDT 2010

Hi Paul,

     The runs are coming along very nicely (so far). I'm right now in Ra 
= 10^7 and see some very interesting dynamics. Thanks for all the advice 
(on a Sunday!).

Regards,
Mani chandra

On 05/16/2010 07:55 PM, nek5000-users at lists.mcs.anl.gov wrote:
>
> Hi Mani,
>
> I find that I need to use something like:
>
>       argt = (t8-time)/0.05
>       if (time.gt.t8) ra = 1.e7 + 0.9e8*(1-exp(argt))
>
> to get the run to transition smoothly to the higher Ra
> values, but this seems to work.
>
> Paul
>
>
>
> On Sun, 16 May 2010, nek5000-users at lists.mcs.anl.gov wrote:
>
>>
>> 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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