[CIG-SHORT] on the viscosity coefficient

Mon Apr 19 22:23:26 PDT 2010

Charales,

>This can be derived from the equations in the manual and I have
verified that this is what is used in the code.

Thank you for the verification.

>As far as I know, the value that Yuta Abe used in the analytical
solution probably corresponded to A_M * exp(-Q/RT)... Does that sound
correct? 

No. A correct value that he had to use in the analytical solution was
A=A_M * exp(-Q/RT)*(sqrt(3)/2)**(n-1). 
He did mistakenly use a value of A_T, which equals to (2/3)**n A.
See the pdf file for the details.

Regards,
Ikuo Cho

On Wed, 14 Apr 2010 14:42:55 +1200
Charles Williams <willic3 at gmail.com> wrote:

> 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
> 

-- 
Cho Ikuo <ikuo-chou at aist.go.jp>
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