# [aspect-devel] compressibility in 2d

Juliane Dannberg dannberg at gfz-potsdam.de
Fri Feb 10 13:08:18 PST 2017

```Hi Menno,

we discussed this today (with Wolfgang and Rene), and one argument that
came up was the one that Jonathan just mentioned.

To make sure, we also checked how other people do this (like how the
equations are written down for example in Turcotte, Schubert and Olson),
and everywhere we looked, the 3 was also written down as a 3 (and not in
dependence of the dimension).

As we also have a 2D compressible benchmark case (the Tan Gurnis '07
benchmark), which has an analytical solution, and we converge to that
solution with the expected rate, we can also be reasonably sure that we
have implemented this in a way that other people think is correct.

interpreting a 2D model as a model that actually is 3D, but infinitely
long in the third dimension and without any changes in properties in
that direction.

Cheers,
Juliane

On 02/10/2017 01:41 PM, Jonathan Perry-Houts wrote:
> Hey Menno,
>
> I'm pretty sure the reason is that 2d models are supposed to represent a
> slice through an infinite-depth 3d model, so the equations do not
> change. This bothered me at first too, and that's how I justified it to
> myself. Hopefully someone else can confirm or deny that justification.
>
> -JPH
>
> On 02/10/2017 06:04 AM, Menno Fraters wrote:
>> Hello all,
>>
>>
>> I have been looking at the formulation of the compressibility in aspect
>> and in the manual there is a 1/3 in front of the div(u)*1* in equation
>> 1. I would expect that this is only valid in 3d, because I think it
>> stems from the deviator which is deviator(*epsilon*) = *epsilon* - 1/dim
>> * trace(*epsilon*)*1*. So I would expect it to be 1/2 in 2d. But I found
>> that in the code it is hardwired as 2/3 (where the 2 comes from I
>> understand).
>>
>>
>> Can someone explain me why this is 2/3 and not 2/2 = 1?
>>
>>
>> Many thanks!
>>
>>
>> Cheers,
>>
>>
>> Menno**
>>
>>
>>
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>>
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```