[aspect-devel] Internal heating in aspect

[Rene Gassmoeller]

Hi Max,

let me cc this to the mailing list, as it might be of interest to others.

I found this old email thread on the mailing list that seems to discuss 
the same issue: 
http://lists.geodynamics.org/pipermail/aspect-devel/2012-November/000138.html 
(there are some additional messages when you scroll through the thread). 
In short: At the time Ian found that this is a problem when the boundary 
layer is underresolved. Since the element at the surface are larger than 
the elements at the CMB they do resolve a different temperature gradient 
for the boundary layer if the boundary layer is not sufficiently 
resolved, and we compute the heat flux based on the temperature gradient.

However, thinking about it again, I do not think this can be the only 
reason. If the difference were caused by numerical resolution alone, the 
average temperature should change, until the two heat fluxes are in 
balance as you mentioned. But another idea I had was that the computed 
heat flux is a postprocessor that only considers physical diffusion 
(i.e. diffusion due to thermal conductivity), while in the assembly we 
also include the numerical diffusion to stabilize the equation. So maybe 
the difference between the heat fluxes is caused by numerical diffusion 
(and it is so large because the cells are relatively coarse)? If that 
were the case the difference should increase/decrease with higher/lower 
resolution, as the stabilization scales with the element size. 
Unfortunately that is not a criterion to distinguish between the two 
possible causes (obviously resolution of the temperature gradient across 
the boundary layer also scales with element size). You could try to 
re-run the model with discontinuous temperature elements, that should 
disable the numerical diffusion. Let me know if that makes sense.

Best,

Rene


On 08/24/2018 06:46 PM, Max Rudolph wrote:
> Rene and Wolfgang,
> We're running some models in 3D spherical geometry in aspect with 
> internal heating and are unable to reproduce thermal histories 
> consistent with what we saw in identically configured calculations in 
> CitcomS. It is possible that there is some aspect of our model setup 
> that is inconsistent, but we are using the same depth profile of 
> viscosity, same boundary conditions, and same initial conditions. The 
> ASPECT models cool much faster (which also drives up viscosity). We 
> are trying to get understand these results, and I was looking at the 
> heat transport in the 3D spherical model discussed in section 5.3.2 of 
> the aspect manual 'simple convection in the 3D spherical shell'. In 
> figure 40, it appears that this calculation has been run to nearly 
> statistically steady state. Is this correct? I am wondering, 
> basically, how to interpret the imbalance between reported surface and 
> CMB heat flow. To follow up on this, I ran the cookbook .prm file from 
> 5.3.2 (shell_simple_3d) for 5 Gyr, which appears to be very close to 
> or at statistically steady state at the end of the calculation. Due to 
> resource constraints, I only ran at global refinement level 3 
> (definitely under-resolved, mea culpa). However, at the end of the 
> calculation, there is still a significant imbalance between the 
> surface and core mantle boundary heat flows. This is a model with no 
> internal heating, so at statistically steady state, the surface and 
> cmb heat flows should balance to conserve energy. Do you have any 
> insight into why we might be seeing this behavior? I've attached the 
> input .prm file, the statistics file, and a plot showing the average 
> temperature and surface and cmb heat flows. Thank you for thinking 
> about this!
>
> Best
> Max
>
> p.s. I sent this to both of you because it looked to me like Wolfgang 
> contributed the cookbook. Please let me know if there is someone else 
> that might be better positioned to help with this.
>
> image.png
>
>
>

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

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