[CIG-SHORT] on the viscosity coefficient

Sun Apr 25 17:02:51 PDT 2010

Charles,

I'm sorry for the delay.

> A_ET = (2/3)^n * A,
> which I believe is what was used by Yuta Abe.  Does this sound correct?
> p.s.  The value of A_ET is what is used as input for PyLith 1.4.2 (and an upcoming version 1.4.3).  

Yes. Yuta Abe substituted a value of A_ET as A in equation 
> epsilondot_11 = A * S_1^n.

It was a mistake but he obtained a good fit between the numerical and
analytical solutions. This is exactly the problem I wanted to solve.

Regards,

Ikuo Cho

On Fri, 23 Apr 2010 09:54:38 +1200
Charles Williams <willic3 at gmail.com> wrote:

> Ikuo Cho,
> 
> Thanks very much for your detailed explanation.  After going through your explanation, it appears that the difficulty arises through a difference in how we define the power-law exponent.  Using the following definitions:
> 
> A_ET = A_E * exp(-Q/(R*T))
> sigma_d = sigma_1 - sigma_3
> 
> PyLith 1.4.2 defines the flow law as:
> 
> epsilondot_11 = A_ET * sigma_d^n
> 
> In the derivation of Yuta Abe, the flow law used is:
> 
> epsilondot_11 = A * S_1^n
> 
> The differences arise because in the case of PyLith, the flow law is a function of the differential stress, while in the case of the derivation of Yuta Abe, the flow law is a function of the maximum deviatoric stress (S_1).  The relationship between the two is:
> 
> S_1 = 2 * sigma_d/3
> 
> Combining the two equations for epsilondot_11, we get
> 
> A_ET = (2/3)^n * A,
> 
> which I believe is what was used by Yuta Abe.  Does this sound correct?
> 
> Thanks,
> Charles
> 
> p.s.  The value of A_ET is what is used as input for PyLith 1.4.2 (and an upcoming version 1.4.3).  In the next major release of PyLith, a different set of parameters will be used to define power-law flow.
> 
> On 20/04/2010, at 5:23 PM, Ikuo Cho wrote:
> 
> > 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>
> > <equation.pdf>
> 
> 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>