[aspect-devel] Internal heating in aspect (Ludovic Jeanniot)
Elbridge Gerry Puckett
egp at math.ucdavis.edu
Wed Aug 29 16:59:47 PDT 2018
Hi Max,
Here they are. Please let me know what your reaction is.
I have another paper, this is with Jon Robey and involves interface
tracking only, where one reviewer is asking for us to quantify the
effect of the Péclet number in the temperature equation. I'm not quite
sure where the reviewer is coming from ...
Thanks,
- Gerry
On 08/29/2018 04:11 PM, Max Rudolph wrote:
> Gerry,
> Could you please send me the talk slides?
>
> We have had some problems with over/undershoots using DG, even when
> using the bound preserving limiter in aspect. These are not small
> overshoots either. A recent case had min/max values of -0.36 and 1.37
> even though the bound preserving limiter was set to [0,1].
>
> Max
>
> On Wed, Aug 29, 2018 at 2:17 PM Elbridge Gerry Puckett
> <egp at math.ucdavis.edu <mailto:egp at math.ucdavis.edu>> wrote:
>
> Hi Everyone,
>
> I'm sorry to come to this discussion so late. I have been meaning
> to read the entire sequence of posts before posting myself.
>
> Ying He implemented DG with a Bound Preserving (BP) Limiter for
> the temperature equation (with incomprehensible flow). We (Ying,
> Magali, Louise, and myself) submitted a poster to the 2016 AGU
> fall meeting and it was chosen for a talk, which Ying gave.
>
> I have the talk slides and they appear to be relevant to to this
> discussion, even though we did not study internal heating. Again,
> I would have liked to read the entire discussion before posting,
> but Max just mentioned DG and hence it seems appropriate for me to
> offer Ying's talk slides to the [aspect-devel] mailing list as
> well as the rest of the community.
>
> A few words about what Ying / we did. Ying was interested in
> studying the effectiveness of this new methodology as a function
> of the Péclet number (Pe) number. For many of the problems we
> were computing as a group, such as our recent LLSVP paper in the
> special issue of PEPI to associated with the 15th SEDI conference,
> we (Ying) determined that at that Péclet number the changes to our
> results were negligible when one used the original algorithm in
> ASPECT with EV and the new DGBP algorithm.
>
> However, for other problems, Magali had an argument that for some
> problems one might want to compute in ASPECT there would be an
> /effective local Péclet number, /for which there are decided
> differences between the two algorithms. This difference is shown
> in the talk slides. (There is a movie of this, which I can
> probably find.)
>
> I don't see this material in the manual, which is unfortunate. I
> can put this on my to-do list if others think it would be helpful.
>
> Two things to note:
>
> 1. Part of Ying's to-do list was to add the ability to use
> AMR to algorithm with this DGBP temperature
> advection-diffusion algorithm, which I think remains to be
> done.
>
> 2. Another issue to note is that that Ying found it necessary
> to use a second-order accurate Strong Stability Preserving
> time stepping algorithm (SSP2) instead of the usual BDF2
> for the DGBP algorithm. This is from Ying's 2017 PEPI
> paper with Magali and me.
>
> "For the case when the FEM is used for the spatial
> discretization, we use the same semi-implicit BDF2
> scheme as shown in Kronbichler et al. (2012) except we
> fix the time-step size dt for simplicity. However, if
> the DG method is used, then a Strong
> Stability-Preserving (SSP) high order time
> discretization method (Gottlieb, 2005; Gottlieb et
> al., 2001) is applied in order to maintain the bound
> preserving property from the limiter."
>
> This does not seem to be mentioned in the talk slides, probably
> due to lack of time. A search on SSP2 in the ASPECT manual
> generated June 22, 2018 yields zero hits and and even a search on
> DGBP yields only three hits in thre parameter section. There is
> probably room for more documentation there. : -(
>
> Anyway, the point is that one might keep (1) and (2) in mind while
> using DGBP for the temperature equation.
>
> In summary, I didn't intend to write such a long post, I hope some
> of you find it is worthwhile.
>
> Shall I post the talk slides and if so, where? I can put them on
> math.ucdavis.edu/~egp/. <http://math.ucdavis.edu/%7Eegp/.>.. or
> post to this discussion with the slides appended, or ..
>
> Sincerely,
>
> - Gerry
>
>
> On 08/29/2018 12:49 PM, Max Rudolph wrote:
>> Rene,
>> Thank you for summarizing the current state of affairs. I would
>> suggest that when you make the changes in (1)-(2), you also make
>> ASPECT print at least a warning when the entropy viscosity
>> exceeds, say, 1% of the thermal conductivity. It might be even
>> better for the code to exit in with an error unless a parameter
>> is explicitly set to ignore such a condition.
>>
>> It also seems that one way around (1) is to use DG elements for
>> composition. Is this what most users are doing anyways?
>>
>> Thank you for addressing these issues so quickly. I am happy to
>> help with testing as needed.
>>
>> Best,
>> Max
>>
>> On Wed, Aug 29, 2018 at 12:16 PM Rene Gassmoeller
>> <rene.gassmoeller at mailbox.org
>> <mailto:rene.gassmoeller at mailbox.org>> wrote:
>>
>> Hi all,
>>
>> I think by now we have a pretty good understanding of the
>> problem, however there is no clear path forward yet. I have
>> done some further testing with the shell_simple_3d cookbook:
>>
>> - As Max pointed out the artificial viscosity at resolution
>> <= 2 global refinement in spherical models is bigger than the
>> natural diffusion, although it reduces drastically with
>> resolution (compare to a natural conductivity of ~4 W/m*K).
>>
>> Global refinement / Maximum artificial viscosity timestep 0 /
>> timestep 2:
>>
>> 1 (4 radial elements): 94.1 W/m*K / 59.9 W/m*K
>>
>> 2 (8 radial elements): 48.9 W/m*K / 6.12 W/m*K
>>
>> 3 (16 radial elements): 24.8 W/m*K / 0.92 W/m*K
>>
>> There are some pitfalls here, in particular the artificial
>> viscosity in the output of timestep 0 is in general much
>> bigger than in later timesteps (and it only scales linearly
>> with cell size), because we do not have a velocity solution
>> yet. Timestep 1 is somewhat unreliable as well, because the
>> BDF2 scheme is not fully initialized. Nevertheless, for later
>> timesteps the artificial viscosity scales at least with cell
>> size squared (h^2) as expected (actually slightly better,
>> because it is not only h^2, but also based on the residual of
>> the equation, which reduces as well, ideally with h^3). This
>> means higher resolutions should significantly reduce the
>> total amount of artificial diffusion, although it might still
>> be significant (>1% of total diffusion) up to resolution 4 or
>> so, which seems unacceptably expensive. Moreover, as Scott
>> and Cedric mentioned there will always be an imbalance
>> between the heat fluxes at the top and bottom boundary with
>> this method, unless we use radially uniformly spaced
>> elements, or disable the stabilization, although the
>> magnitude of the imbalance should reduce with increased
>> resolution. Also the thermal conductivity within the domain
>> will be unequally distributed (artificial conductivity in the
>> upper mantle will be higher than in the lower mantle).
>>
>> While the above point suggests that the artificial viscosity
>> scheme is correctly implemented, there still exist three
>> points for possible improvements:
>>
>> - As Wolfgang mentioned the parameters that were originally
>> chosen for the artificial viscosity scheme were different
>> from what they are today, because we noticed that the
>> original smoothing was too weak to stabilize oscillations in
>> compositional fields. It is completely possible that the
>> original values were sufficient for the temperature (which
>> already has natural diffusion), and in hindsight I should
>> have thought of just using different parameters for
>> composition and temperature (though that was 6 years ago, and
>> I was just a 2nd year PhD student at the time I worked on
>> modifying the parameters for stabilizing the composition
>> equation). I can easily make a change that allows for
>> different parameters for temperature and composition, which
>> would allow everyone to test their favorite values, without
>> risking oscillations in compositional fields.
>>
>> - Even if we can reduce the parameters it is of course
>> possible that as Max pointed out the anisotropic nature of
>> the diffusion in SUPG is more appropriate / "less wrong" than
>> the isotropic entropy viscosity for our problem. As Juliane
>> and Timo pointed out we could reimplement the content of
>> https://github.com/geodynamics/aspect/pull/412 and see if
>> SUPG performs better for low resolutions. Does anyone know if
>> the "artificial viscosity" of SUPG also scales with h^2?
>> Because if it is linear, we might implement something that is
>> better for low resolutions, but worse for high resolutions.
>>
>> - As Max mentioned: We should not need a stabilization for
>> pure conduction problems (where velocity is 0), and should
>> modify the algorithm accordingly.
>>
>>
>> So the next steps could be:
>>
>> 1. Allow for different stabilization parameters for
>> temperature and composition, and check which values are still
>> stable.
>> 2. Do not stabilize advection/diffusion solutions where the
>> velocity is zero (because it is only a diffusion equation).
>> 3. Reimplement the SUPG based on
>> https://github.com/geodynamics/aspect/pull/412 and see how it
>> performs (at low and high resolutions).
>>
>> Does that summarize our discussion appropriately? I can
>> easily make the code adjustments 1 and 2 (they are easy and
>> useful in any case), and could also look into creating an
>> initial version of 3 (although it would take a bit of time),
>> but I currently do not have the time for much testing of the
>> methods, so I would be greatful if someone else could do the
>> testing and benchmarking of the methods.
>>
>> Best,
>> Rene
>>
>>
>> On 08/29/2018 09:19 AM, Max Rudolph wrote:
>>> On Tue, Aug 28, 2018 at 8:01 PM Wolfgang Bangerth
>>> <bangerth at colostate.edu <mailto: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
>>> <mailto:bangerth at colostate.edu>
>>> www:
>>> http://www.math.colostate.edu/~bangerth/
>>> <http://www.math.colostate.edu/%7Ebangerth/>
>>>
>>>
>>>
>>> _______________________________________________
>>> Aspect-devel mailing list
>>> Aspect-devel at geodynamics.org
>>> <mailto:Aspect-devel at geodynamics.org>
>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/aspect-devel
>>
>> --
>> Rene Gassmoeller
>> https://gassmoeller.github.io/
>>
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>>
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