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

[Wolfgang Bangerth]

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
                            www: http://www.math.colostate.edu/~bangerth/