[CIG-SHORT] on the viscosity coefficient

Tue Apr 13 19:42:55 PDT 2010

Dear Ikuo,

I apologize for being so slow to respond to this.  I just returned from a trip and have started looking at things.  I'm still somewhat puzzled.  Internally, PyLith 1.4.2 uses a viscosity-coefficient, which can be defined as:

viscosity-coefficient = (1/(A_T * sqrt(3)**(n+t)))**(1/n)

This can be derived from the equations in the manual and I have verified that this is what is used in the code.  As far as I know, the value that Yuta Abe used in the analytical solution probably corresponded to A_M * exp(-Q/RT), which should be A_T * sqrt(3)**(n+1)/2.  Does that sound correct?  It's also possible that the power-law-coefficient used in his analytical solution is defined differently.  Let me know what you think about this, because it would be good to get this resolved.

Thanks,
Charles

On 17/03/2010, at 11:03 PM, Ikuo Cho wrote:

> Charles,
> 
> I discussed with my colleague, Yuta Abe, on the fit between the final
> output from PyLith 1.4.2 and an analytical solution.
> 
> Yuta Abe Wrote:
>> By the way, the final output of the PyLith program coincided with
> the analytical solution.
> 
> We found that an input parameter for the analytical calculation was
> incorrect when he wrote the above report, and consequently analytical
> solution does not fit the  numerical results. He did use a value of A_T
> as both the "powerlaw-coefficient" for PyLith and a parameter value for
> the analytical calculation, although he had to use values of A_T and
> (3/2)**n A_T for the "powerlaw-coefficient" and the analytical
> calculation, respectively.
> (As the result, he observed a good fit between the numerical and
> analytical solutions.)
> 
> I wanted to ask from this fact the possibility that the
> "powerlaw-coefficient" is actually defined by A_T'=(3/2)**n A_T,
> instead of A_T defined in (5.75) in PyLith 1.4.2.
> Is it difficult to check?
> 
> By the way, I recently installed PyLith from the repository. I also made
> comparison between the numerical and the analytic solutions for the same
> problem. (I noticed a small difference in the definition of A_T between
> the released and repository versions.)
> They showed a good fit in this case. 
> 
> Ikuo Cho
> 
> On Fri, 5 Mar 2010 07:14:30 +1300
> Charles Williams <willic3 at gmail.com> wrote:
> 
>> Dear Yuta Abe,
>> 
>> I will look at the code and the manual to see if there is a problem.  As I mentioned in a previous e-mail to cig-short, we are changing the input parameters for power-law materials, so 'eta' will no longer be a parameter in upcoming versions.  I will let you know what I find out about version 1.4.2, though.
>> 
>> I'm glad the final output matches the analytical solution.  Would it be possible for you to describe the problem?  It may be useful as an example problem or benchmark.
>> 
>> Cheers,
>> Charles
>> 
>> On 4/03/2010, at 9:07 PM, Yuta Abe wrote:
>> 
>>> Dear PyLith Developers:
>>> 
>>> I have a question about the viscosity_coefficient "eta", which is one of the physical properties that you get in the output "cel_info_fields" when you carry out analysis of a power-law viscoelastic material using PyLith 1.4.2.
>>> 
>>> I thought the values of "eta" could be calculated using the equations (5.74), (5.75) and (5.76) by substituting the power-law coefficient "At" and the power-law exponent n. I substituted "At"=1.99e-41 and n=3 into those equations, and obtained " eta"=1.77e+13 as a result. However, the value of "eta" in info.vtk file which was obtained as an automatic output of the PyLith program for the same values of "At"=1.99e-41 and n=3 was "eta"=1.77e+18, 100,000 times as large as the above value. By the way, the final output of the PyLith program coincided with the analytical solution.
>>> 
>>> I would like to find out the origin of this difference, so please kindly tell me how the value of "eta" is calculated within the PyLith program.
>>> 
>>> 
>>> ------------------------------------------------------
>>> Yuta ABE
>>> Active Fault and Earthquake Reserch Center
>>> National Institute of Advanced Industrial Science and Technology,Japan
>>> tel; +81-29-861-3686
>>> email; yuta-abe at aist.go.jp
>>> -------------------------------------------------------  
>>> _______________________________________________
>>> CIG-SHORT mailing list
>>> CIG-SHORT at geodynamics.org
>>> http://geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>> 
>> Charles A. Williams
>> Scientist
>> GNS Science
>> 1 Fairway Drive, Avalon
>> PO Box 30368
>> Lower Hutt  5040
>> New Zealand
>> ph (office): 0064-4570-4566
>> fax (office): 0064-4570-4600
>> C.Williams at gns.cri.nz
>> NOTE NEW E-MAIL ADDRESS
>> 
> 
> ----------------------------------------------------------
> Ikuo Cho  ( ikuo-chou at aist.go.jp )
> Geological Survey of Japan,
> National Institute of Advanced Industrial Science and Technology
> Tsukuba Central 7, Tsukuba 305-8567 Japan
> Tel +81-29-861-3891, Fax +81-29-861-3682
> ----------------------------------------------------------
> 

Charles A. Williams
Scientist
GNS Science
1 Fairway Drive, Avalon
PO Box 30368
Lower Hutt  5040
New Zealand
ph (office): 0064-4570-4566
fax (office): 0064-4570-4600
C.Williams at gns.cri.nz
NOTE NEW E-MAIL ADDRESS

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