[aspect-devel] Internal heating in aspect (Ludovic Jeanniot)

Rene Gassmoeller rene.gassmoeller at mailbox.org
Tue Sep 11 11:44:27 PDT 2018


Scott,

I have opened the pull request with the improved heat flux computation, 
and it is available here: 
https://github.com/geodynamics/aspect/pull/2660 . It already includes 
the improvements Wolfgang made to the advection stabilization term, so 
this should be a good version to start the testing.

I have run into some issues trying to reproduce compressible benchmark 
results with the new method though (I explain them in the pull request), 
I do not suppose you have another magic fix for them at hand? That would 
be much appreciated :-).

Best,

Rene


On 09/06/2018 07:18 PM, Scott King wrote:
> Great!   Glad I could contribute instead of being my usual grumpy PITA.
>
> We’re all set up to run Zhong cases as quickly as we can get them 
> through the queues.
>
> Best
>
> Scott
>
> Sent from my iPhone
>
> On Sep 6, 2018, at 10:08 PM, Rene Gassmoeller 
> <rene.gassmoeller at mailbox.org <mailto:rene.gassmoeller at mailbox.org>> 
> wrote:
>
>> Hi Scott,
>>
>> very interesting, thanks for sharing that thought! That looks like a 
>> significant improvement for the heat flux postprocessors. You were 
>> right, the changes to the postprocessor were not very complicated, 
>> and I will open a pull request for them tomorrow, when I have cleaned 
>> up a few things. I just wanted to share some first results with you:
>>
>> These are the original convergence studies for the Blankenbach 1a 
>> case with ASPECT:
>>
>> # Nu                     Vrms                    name (refinement level):
>> 4.78661864e+00 4.34590432e+01 case1a_ref4.stat
>> 4.87927972e+00 4.29377468e+01 case1a_ref5.stat
>> 4.88993106e+00 4.28733838e+01 case1a_ref6.stat
>> 4.88680525e+00 4.28659548e+01 case1a_ref7.stat
>> 4.88440900e+00 4.28649470e+01 case1a_reference.stat
>>
>> Both Nu and Vrms converge, but rather slowly for the very low 
>> Rayleigh number (10^4). Below are the values with Wolfgang's 
>> improvements in pull request 2650 (taking the max of artificial 
>> diffusion and physical diffusion instead of the sum):
>>
>> # Nu                     Vrms                    name (refinement level):
>> 5.30885322e+00 4.28499932e+01 case1a_ref3.stat
>> 5.06735289e+00 4.28656773e+01 case1a_ref4.stat
>> 4.93712396e+00 4.28650353e+01 case1a_ref5.stat
>> 4.88440900e+00 4.28649470e+01 case1a_reference.stat
>>
>> As you can see the Vrms is now much closer to the reference value 
>> already at low resolutions (even at refinement level 3, which is only 
>> 8x8 cells). But the Nusselt number is now worse, and converging from 
>> above the reference value instead of from below. With your suggested 
>> improvements to the postprocessors (taking the volume averaged total 
>> heat flux in the boundary cell, instead of the conductive heat flux 
>> at the surface):
>>
>> # Nu                     Vrms                    name (refinement level):
>> 4.89728221e+00 4.28499932e+01 case1a_ref3.stat
>> 4.88535143e+00 4.28656773e+01 case1a_ref4.stat
>> 4.88443365e+00 4.28650353e+01 case1a_ref5.stat
>> 4.88440900e+00 4.28649470e+01 case1a_reference.stat
>>
>> The Vrms is not affected, because it is only a change in the 
>> postprocessor, but now the Nu number is significantly closer to the 
>> reference value even at low resolutions. All in all, we now get a 
>> better accuracy with a 16x16 grid, than with a 128x128 grid before 
>> the changes. I would say that is progress :-).
>> The other Blankenbach cases show similar improvements (still running 
>> though), and I have not yet tested the behavior for other geometries, 
>> but I do not think there is a conceptual problem. I will not have 
>> time to do much more benchmarking, because I am traveling from the 
>> end of next week on, but do you think you or Grant would have some 
>> time to give a few of the cases of the Zhong 2008 paper another try 
>> once the changes are in the main version?
>>
>> Thanks again for the reference!
>>
>> Best,
>> Rene
>>
>> On 09/05/2018 04:47 PM, Scott King wrote:
>>>
>>> As for calculating fluxes at the boundaries, I looked at the heat 
>>> flux code a bit and I’m wondering...  I will share this paper with 
>>> you all.
>>>
>>> https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1365-246X.1987.tb01375.x
>>>
>>> It might be less relevant to second-order elements than linear 
>>> elements but, a lot of the same arguments I’m seeing in the posts 
>>> the last few days are bringing back memories.   This is what is done 
>>> by default in CitcomS (unless you explicitly call the CFB method).   
>>> I suspect it should be fairly trivial for someone who is good with 
>>> deal.ii to implement because it is pretty standard finite element 
>>> stuff, i.e., calculate fluxes at the internal integration points and 
>>> project the values to the nodes.
>>>
>>> Yes, the artificial diffusivity is an issue but I think this 
>>> explains why even when we turn it off we get relatively poor Nusselt 
>>> numbers while getting excellent agreement with depth-averaged 
>>> properties and mean values.
>>>
>>> Scott
>>>
>>>> On Sep 5, 2018, at 2:56 PM, Max Rudolph <maxrudolph at ucdavis.edu 
>>>> <mailto:maxrudolph at ucdavis.edu>> wrote:
>>>>
>>>> OK, you are right that there will always be some region with more 
>>>> artificial than physical heat transport.
>>>> What about instead looking at the ratio of physical to artificial 
>>>> heat flux through each boundary?
>>>> For Rene's anisotropic "SUEV" implementation, even in the presence 
>>>> of large entropy viscosity, the artificial heat transport can be 
>>>> very small as long as u.gradT is small. In particular, even though 
>>>> entropy viscosity is fairly large at the boundaries, the velocities 
>>>> are tangential to the boundary, so there is very little artificial 
>>>> diffusion.
>>>>
>>>> Max
>>>>
>>>> On Wed, Sep 5, 2018 at 10:41 AM Wolfgang Bangerth 
>>>> <bangerth at colostate.edu <mailto:bangerth at colostate.edu>> wrote:
>>>>
>>>>     On 09/05/2018 07:12 AM, Max Rudolph wrote:
>>>>     >
>>>>     > Rene and I discussed this idea on Monday and I don't think
>>>>     that this is
>>>>     > the right thing to do. It would lead to an unexpected
>>>>     relationship
>>>>     > between the temperature gradient (and hence temperature
>>>>     structure of the
>>>>     > lithosphere) and the physical thermal conductivity. Maybe
>>>>     more helpful
>>>>     > would be a separate output of the non-physical contribution
>>>>     to the heat
>>>>     > flux through each boundary, or within the entire domain as
>>>>     the ratio of
>>>>     > the norm of the artificial heat flux divided by the norm of
>>>>     the total
>>>>     > heat flux. I still think that a warning message when this
>>>>     quantity
>>>>     > exceeds, say, 1% would help users understand that they should
>>>>     expect
>>>>     > unphysical results.
>>>>
>>>>     But this warning message would be printed on pretty much every
>>>>     single
>>>>     simulation in which the mesh does not completely resolve
>>>>     boundary and
>>>>     internal layers -- which is essentially every simulation ever
>>>>     done in
>>>>     the field of mantle convection.
>>>>
>>>>     If it was a rare occasion where artificial viscosity is needed
>>>>     to make a
>>>>     simulation stable, then we wouldn't use it. But the reality is
>>>>     that all
>>>>     realistic global-scale simulations must necessarily have some
>>>>     kind of
>>>>     artificial diffusion (SUPG, EV, dG schemes, ...) that is larger
>>>>     than the
>>>>     physical diffusion at least in parts of the domain because
>>>>     resolving the
>>>>     boundary layers is not possible on a global scale and will not be
>>>>     possible for a long time to come. The idea of artificial diffusion
>>>>     schemes is to make boundary layers as large as the cells of the
>>>>     mesh so
>>>>     that they are resolved, rather than leading to
>>>>     over/undershoots. It is
>>>>     *needed* to avoid Gibb's phenomenon if you can't make the mesh
>>>>     small enough.
>>>>
>>>>     That does not mean that (i) the scheme we currently use is the
>>>>     best
>>>>     idea, (ii) we can't improve the situation. But I do not think that
>>>>     printing a warning for essentially every single simulation is
>>>>     useful.
>>>>
>>>>     (I'll note that we also use artificial diffusion schemes for the
>>>>     compositional fields for which the physical diffusion is zero
>>>>     -- so the
>>>>     artificial diffusion is *always* larger than the physical one.)
>>>>
>>>>     Best
>>>>       W.
>>>>
>>>>     -- 
>>>>     ------------------------------------------------------------------------
>>>>     Wolfgang Bangerth          email: bangerth at colostate.edu
>>>>     <mailto:bangerth at colostate.edu>
>>>>                                 www:
>>>>     http://www.math.colostate.edu/~bangerth/
>>>>     <http://www.math.colostate.edu/%7Ebangerth/>
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>>>
>>>
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>>
>> -- 
>> Rene Gassmoeller
>> https://gassmoeller.github.io/

-- 
Rene Gassmoeller
https://gassmoeller.github.io/

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