[Nek5000-users] RB convection with high Rayleigh numbers

Sun May 16 09:25:04 CDT 2010

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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