[aspect-devel] Help needed with setting up an EBA benchmark

[Ian Rose]

(Resending due to mailing list issues)
Hi Wolfgang and all,

Excuse the overly verbose answer, I'm talking this out as much for me as
anyone.  So, thermodynamically, the adiabatic heating term is sensitive to
the total temperature rather than differences in temperature (as in, for
instance, the buoyancy).  I see that at the top of page three they have
defined T_0 to be the dimensional surface temperature over the temperature
scale, \Delta T.  In the anelastic case there would be an adiabatic profile
starting from T_0, but in this case, because it is incompressible, the
reference temperature is T_0 all the way down.

The way it shakes out in these equations, T_0 becomes a free parameter that
can increase or decrease the effect of adiabatic heating on the model.  For
the benchmark case, they use T_0 = 273/3000, like you said, but I could put
in anything, really.  All this is a long way of saying that in your
parameter file you have set the boundary conditions for temperature to go
from zero to one at the bottom.  To my eyes, it looks like you can
reproduce the conditions of the benchmark by simply changing the
temperature boundary conditions to 0.091 - 1.091.

I'm not sure if that made sense, but hopefully it did.
Best,
Ian


On Thu, Sep 4, 2014 at 6:10 PM, Katrina Arredondo <karredondo at ucdavis.edu>
wrote:

> I guess I was puzzled by your question on how to nondimensionalize the
> energy equation because I've planned to test EBA in ASPECT using the
> dimensional equations. I didn't word my confusion well. To me ASPECT equals
> dimensional terms and equations, but I suppose a nondimensional form could
> be good for testing. However, if that becomes an option, users may
> consistently choose to use the nondimensional form over the dimensional
> form because it's "easier." As is we are being forced to translate
> everything into dimensional form.
>
>  If we want to test dimensional vs nondimensional we would probably need
> to change the code as written in ASPECT.  The changes will be more extreme
> if latent heat is included. Without latent heat we would still need to add
> the Dissipation and Raleigh number and extra temperature term multipliers
> into the momentum and energy equations.
>
> T0 is defined by the user and is usually the surface temperature or 0
> Celsius. The benchmark is giving the nondimensional form of that number.
>
> In my incomplete subduction models, I added T0 to my ASPECT viscosity and
> temperature modules because it is a commonly used term. In my ASPECT and
> CitcomS input decks, T0 is defined by the user (me).
>
> Here at Davis the ASPECT discussion group has repeatedly asked ourselves
> what is the best way to translate the dimensional terms in ASPECT into the
> nondimensional Rayleigh and Dissipation numbers during postprocessing. If
> that still isn't well defined I can bring it up at the next meeting or ask
> Prof. Don Turcotte. Many of the terms used to define those numbers, such as
> delta T in the Rayleigh number, are also used elsewhere in the initial
> model to define the initial temperature field, etc while other terms like
> the thermal expansivity could be chosen as the average throughout the
> model.
>
>  We can help you with this.
>
>  - Katrina
>
>
>
>
> On Thu, Sep 4, 2014 at 5:18 PM, Wolfgang Bangerth <bangerth at tamu.edu>
> wrote:
>
>> On 09/04/2014 07:09 PM, Katrina Arredondo wrote:
>>
>>> But why does it need to be nondimensionalized? Just to be consistent
>>> with the benchmark?
>>>
>>
>> It doesn't have to be. The benchmark is defined in terms of
>> nondimensional quantities -- it is what it is. But ASPECT does not take
>> Rayleigh and Dissipation numbers as inputs. I have to somehow translate
>> them into the physical quantities.
>>
>>
>>
>> > I guess I was thinking that this could be a test for how "easy" it is
>> > to translate the geodynamics nondimensional terms into dimensional
>> > terms in ASPECT. Otherwise why have the dimensional terms at all, if
>> > it's too hard.
>>
>> Because the real world is sufficiently complicated that
>> nondimensionalization does not work. (For example, what exactly is the
>> Rayleigh number when you have variable gravity, a geometry for which there
>> is no obvious lengthscale, and thermal expansion and viscosity depend
>> strongly on the temperature?) I think the better question is why we should
>> have the nondimensional form if it only describes idealized but
>> non-realistic situations :-)
>>
>> Best
>>  Wolfgang
>>
>>
>> --
>> ------------------------------------------------------------------------
>> Wolfgang Bangerth               email:            bangerth at math.tamu.edu
>>                                 www: http://www.math.tamu.edu/~bangerth/
>>
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>>
>
>
>
> --
>
> Katrina Arredondo
> Ph.D. Candidate
> Geodynamics/Subduction Zones
> University of California, Davis
> Department of Geology
> One Shield Avenue, Davis CA 95616
>
>
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>
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