[aspect-devel] Checkerboard at large scale
Juliane Dannberg
judannberg at gmail.com
Sat Apr 7 13:09:43 PDT 2018
Hi Lev (and everyone else),
I think that if the problem is indeed what is described in this issue
<https://github.com/geodynamics/aspect/issues/1872>, assuming your model
is _incompressible_, your density does not matter. You only have to make
sure that if you integrate the divergence of the velocity over all
boundaries of the model (in finite element space, not just
analytically), you get zero. Or in other words, that there is no net
influx or outflux.
If that is not the case, and all boundaries are closed, you will not get
a reasonable solution (or the model will just not converge). John,
Wolfgang, please correct me if you think that works differently.
You can fix that (as John and Wolfgang suggested) either by using a free
surface (so any net mas influx or ouflux would go into deforming the
surface), or by leaving one boundary (e.g. the bottom) open, so that
material can flow out. If you try this, and get a lot of influx or
outflux through your open boundary (or really strong net topography),
then your boundary conditions aren't even close to zero net influx or
outflux, and you should check if you set the boundary velocity correctly.
If, on the other hand, your model is _compressible_, this would work
differently (so it would be good if you could tell us if it is).
Best,
Juliane
Am 4/7/2018 um 11:14 AM schrieb Lev Karatun:
> Hi Juliane,
>
> (sorry for multiple emails -- meant to use "Reply all" the first time)
>
> thank you for the clarification! I'm still confused unfortunately.
> You're saying
>
> If your model is incompressible, we solve divergence u = 0, which
> basically assumes that the density is constant. So from the point
> of view of the mass conservation equation, material entering the
> model always has the same density as material leaving th model
> ...
> So I guess in this case you should check that you conserve volume
>
>
> But doesn't it contradict what John and Wolfgang are saying (that I
> should balance mass, otherwise I'll see anomalous pressure or
> anomalous topography)?
>
>
> Best regards,
> Lev Karatun.
>
> 2018-04-06 13:20 GMT-04:00 Juliane Dannberg <judannberg at gmail.com
> <mailto:judannberg at gmail.com>>:
>
> Hi Lev,
>
> maybe I phrased that a bit ambiguously, as the model may use
> different densities in different parts of the equations.
>
> If your model is incompressible, we solve divergence u = 0, which
> basically assumes that the density is constant. So from the point
> of view of the mass conservation equation, material entering the
> model always has the same density as material leaving th model.
> However, you might still use a variable density in the buoyancy
> term, and this will also be the density that you see in the
> visualization output, and that is used for postprocessing
> purposes. So the mass flux postprocessor could suggest that the
> sum of mass in/outflux is not exactly zero if the material flowing
> in and out has different densities. So I guess in this case you
> should check that you conserve volume; the mass flux postprocessor
> can still be useful, as the integrated mass flux should still be
> approximately zero (assuming your density does not change too much).
>
> Another idea: From they way you are describing it, the problem is
> essentially 2d (your prescribed velocity at the left/right
> boundary does not change in the 3rd dimension, and all other
> boundaries are free slip). So you could test your setup in 2d, see
> if you get a reasonable solution there, and then go from there.
> That would make testing much faster and simpler.
>
> Best,
> Juliane
>
>
> On 04/06/2018 09:45 AM, Lev Karatun wrote:
>> Hi Juliane,
>>
>> If density of the material entering the model is different from
>> material leaving it, the b.c. can't be both volume and mass
>> conserving. Am I understanding something wrong?
>>
>> Best regards,
>> Lev Karatun.
>>
>> 2018-04-06 2:18 GMT-04:00 Juliane Dannberg <judannberg at gmail.com
>> <mailto:judannberg at gmail.com>>:
>>
>>
>>>
>>> 1. Are the applied boundary conditions mass and/or
>>> volume conserving?
>>>
>>> Volume conserving. To be honest, I never put too much
>>> thought into this -- how do I determine if I should conserve
>>> mass or volume? Is there some sort of rule of thumb?
>> From what you're saying, my guess would be that the boundary
>> conditions could be the problem (as I think John was implying).
>> You can check if if they conserve mass for example by using
>> the mass flux postprocessor; it will give you the mass flux
>> though each of the boundaries. Usually you should conserve
>> mass (and if the model is incompressible, that would also
>> mean conserving the volume).
>>
>> Alternatively, you can also try leaving the top or bottom
>> boundary open and see if material flows in or out there, that
>> will also give you a clue if the boundary conditions you're
>> prescribing at the sides are reasonable.
>>
>> Best,
>> Juliane
>>
>>
>>> 2018-04-02 12:43 GMT-04:00 John Naliboff
>>> <jbnaliboff at ucdavis.edu <mailto:jbnaliboff at ucdavis.edu>>:
>>>
>>> Hi Lev,
>>>
>>> Typically 'checker boarding' is seen in the pressure
>>> field and arises when using plasticity with low-order
>>> (Q1P0) elements. This looks a bit different and could be
>>> related to any number of issues. However, I have not
>>> seen anything like this specifically. From your
>>> description, it sounds like you would expect convergence
>>> in the upper region (lithosphere?) and a downwelling in
>>> the model center that transitions to outflow in the
>>> outflux regions?
>>>
>>> So, a few follow-up questions:
>>>
>>> 1. Are the applied boundary conditions mass and/or
>>> volume conserving?
>>> 2. Are there similar (or other odd) patterns in the
>>> pressure, temperature, etc fields?
>>> 3. What element type?
>>> 4. Linear or non-linear rheology?
>>> 5. If non-linear, did the non-linear solver converge to
>>> a reasonable value?
>>>
>>> Depending on the exact setup, there are a number way to
>>> start going about diagnosing the issue. I would start
>>> with simplifying the material properties and boundary
>>> conditions to make sure you are getting the expected
>>> velocity field. For example, use an isothermal
>>> temperature profile and constant density/viscosity/etc.
>>> This could be done in combination with only applying the
>>> imposed inflow/outflow one one side.
>>>
>>> Cheers,
>>> John
>>>
>>> On 03/29/2018 07:05 PM, Lev Karatun wrote:
>>>> Hi everyone,
>>>>
>>>> I was trying to run some 3-D compression models, but
>>>> all I'm getting is a checkerboard pattern (see
>>>> screenshot attached). Boundary conditions are as follows:
>>>> left, right walls: influx through the top half, outflux
>>>> through bottom.
>>>> all other walls: free slip.
>>>> I tried increasing the resolution but it didn't help. I
>>>> also thought about decreasing the CFL number but the
>>>> instability happens at the first timestep, so it
>>>> doesn't seem relevant. I was wondering if someone faced
>>>> a similar problem in their research? What did you do to
>>>> overcome it?
>>>>
>>>> Thanks in advance!
>>>>
>>>> Best regards,
>>>> Lev Karatun.
>>>>
>>>>
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>>>
>>>
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>>
>> ----------------------------------------------------------------------
>> Juliane Dannberg
>> Project Scientist, UC Davis
>> jdannberg.github.io <https://jdannberg.github.io/>
>>
>>
>>
>
> ----------------------------------------------------------------------
> Juliane Dannberg
> Project Scientist, UC Davis
> jdannberg.github.io <https://jdannberg.github.io/>
>
>
>
----------------------------------------------------------------------
Juliane Dannberg
Project Scientist, UC Davis
jdannberg.github.io <https://jdannberg.github.io/>
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