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

[Max Rudolph]

Wolfgang,
Attached are two images showing the artificial viscosity for the purely
conductive model at global refinement 3 and global refinement 5. The
physical thermal conductivity in these models is 4.7 W/m/K, so for both
models the artificial viscosity is dominant. This explains why these models
evolve so quickly to steady state, and the rate of approach to steady state
is slower for higher mesh resolution. If the artificial viscosity was
uniform, the steady state solution would actually agree with the analytic
solution too, because the steady conduction problem does not depend on k,
provided that k is uniform.

For zero velocity, the aspect default choice for the artificial viscosity
scales with cell diameter. From the information in the visualization
output, it looks like the artificial viscosity at refinement level 5 is
about 1/4 that at refinement level 3, so close to what should be expected.

Max

On Wed, Aug 29, 2018 at 9:19 AM Max Rudolph <maxrudolph at ucdavis.edu> wrote:

> On Tue, Aug 28, 2018 at 8:01 PM Wolfgang Bangerth <bangerth at colostate.edu>
> wrote:
>
>> On 08/28/2018 05:33 PM, Max Rudolph wrote:
>> >  From this, it is very obvious why the solution to the convection
>> problem at
>> > low resolution is very diffusive and also why the interior temperature
>> is much
>> > closer to the surface temperature than to the CMB temperature because
>> the
>> > artificial viscosity is on the order of 20 times larger than the
>> thermal
>> > conductivity near the surface.
>>
>> Would it be easy to verify whether the artificial viscosity ("artificial
>> conductivity") decreases at the expected rate with mesh refinement?
>>
>
> What is the most helpful way for me to show this? Visualization of a
> couple of slices from the 3D conduction model? I tried to get the depth
> average of artificial viscosity but the postprocessor is not implemented.
>
>
>> > For the conduction problem, the default values of the artificial
>> viscosity are
>> > also much larger than the thermal conductivity.
>>
>> I think that's the point worth investigating. Since in this case the
>> velocity
>> is zero, one would expect the artificial viscosity to also be at least
>> quite
>> small. Why is it not?
>>
>
> *Maybe the spherical and 2D annulus geometry models are returning an
> unhelpful length scale, like planetary radius instead of layer depth?*
>
> aspect/source/simulator/entropy_viscosity.cc (starting line 191):
> // If the velocity is 0 we have to assume a sensible velocity to calculate
> // an artificial diffusion. We choose similar to nondimensional
> // formulations: v ~ thermal_diffusivity / length_scale, which cancels
>     // the density and specific heat from the entropy formulation. It seems
>     // surprising at first that only the conductivity remains, but remember
>     // that this actually *is* an additional artificial diffusion.
>     if (std::abs(global_u_infty) < 1e-50)
>       return parameters.stabilization_beta *
>              max_conductivity / geometry_model->length_scale() *
>              cell_diameter;
>
>
>
>>
>> Best
>>   W.
>>
>> --
>> ------------------------------------------------------------------------
>> Wolfgang Bangerth          email:                 bangerth at colostate.edu
>>                             www: http://www.math.colostate.edu/~bangerth/
>>
>>
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