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

[Scott King]

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> 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/~bangerth/>
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