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<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'>Hi John,</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'>Have you tried adding a compressible layer
at the surface of the model?<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'>Nicolas Riel and I ran some extension
models recently and found out that the only way to achieve large deformation is
to use such compressible layer.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'>The initial geometry of the model is as
follow with the compressible layer in red:<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><img width=404 height=156 id="_x0000_i1032"
src="cid:image003.jpg@01CAC06D.9F330650"><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>so you can extend the model quite extensively (the compressible has
been removed for visualisation)<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'><img width=926 height=152 id="_x0000_i1025"
src="cid:image004.jpg@01CAC06D.9F330650"><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'>Give it a go!<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'>Cheers<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=blue face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:blue'>gilly</span></font><o:p></o:p></p>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
</div>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>________________________________________________</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Dr Guillaume Duclaux</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>CSIRO Earth Science and Resource Engineering</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Visiting address: ARRC, 26 Dick Perry Av., <st1:place w:st="on"><st1:City
w:st="on">Kensington</st1:City> <st1:State w:st="on">WA</st1:State></st1:place>
6151</span></font><o:p></o:p></p>
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Box 1130</st1:Street>, <st1:City w:st="on">Bentley</st1:City> <st1:State
w:st="on">WA</st1:State></st1:address> 6102, <st1:country-region w:st="on"><st1:place
w:st="on">Australia</st1:place></st1:country-region></span></font><o:p></o:p></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Ph: + 61 8 6436 8728 Fax: + 61 8 6436
8555 Web: <a href="http://www.csiro.au/">www.csiro.au</a></span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<div class=MsoNormal align=center style='text-align:center'><font size=3
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<hr size=2 width="100%" align=center tabIndex=-1>
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<p class=MsoNormal style='margin-bottom:12.0pt'><b><font size=2 face=Tahoma><span
lang=EN-US style='font-size:10.0pt;font-family:Tahoma;font-weight:bold'>From:</span></font></b><font
size=2 face=Tahoma><span lang=EN-US style='font-size:10.0pt;font-family:Tahoma'>
cig-long-bounces@geodynamics.org [mailto:cig-long-bounces@geodynamics.org] <b><span
style='font-weight:bold'>On Behalf Of </span></b>John Naliboff<br>
<b><span style='font-weight:bold'>Sent:</span></b> Wednesday, 10 March 2010
3:03 PM<br>
<b><span style='font-weight:bold'>To:</span></b> cig-long@geodynamics.org<br>
<b><span style='font-weight:bold'>Subject:</span></b> [CIG-LONG] Convergence
issues with long-term extension models</span></font><span lang=EN-US><o:p></o:p></span></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Hello all, <o:p></o:p></span></font></p>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>I'm hoping to get some input on convergence problems I'm having with 2D
long-term extension models.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>The models are designed following Wijns et al. 2005 (EPSL), who modeled
extension of a brittle upper crust overlying a viscous lower crust using
Underworld. The initial geometry is 160 km (width) x 60 km (depth) and
the upper crust follows a yielding law similar to the DruckerPrager yield criterion.
The boundary conditions are free-slip on all sides, although a weak,
low-density layer is present above the upper crust (i.e. top of lithosphere
should behave in a similar fashion to a true free-surface). Extension is
driven by a fixed velocity of 3 cm/yr applied to the right side of the 2D box.
The models in the paper are run up to roughly 80% extension (~ 4 Myr). <o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>The simulations I'm running mimic the models above very closely,
although I'm using an upper free-surface rather than placing a weak, low-density
layer above the upper crust and specifying free-slip on the top boundary.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>In short, the problem I'm encountering reproducing the long-term
extension models is that my simulations stop converging after ~ 1-2 Myr
(~ 25%-40% extension). In terms of specific error messages, the problem
is almost always related to the Stokes Uzawa Solver (ex: </span></font><span
class=apple-style-span><i><font size=2 face=Helvetica><span style='font-size:
10.0pt;font-family:Helvetica;font-style:italic'>uzawaRhsScale has illegal value
'inf', etc</span></font></i></span><span class=apple-style-span><font size=4
face=Helvetica><span style='font-size:13.5pt;font-family:Helvetica'>).</span></font></span><o:p></o:p></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>In terms of the model output, by 1-2 Myr very large strain rate
gradients have developed at the model surface roughly following horst and
grabben structures. I think this may be the source of the convergence
issue, but at this point I'm really not certain.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>After initially having convergence issues with a resolution of 1 km and
30 particles per cell (ppc), I systematically increased the resolution up 0.25
km with 60 ppc, but all the models still stopped converging between 1-2 Myr.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>I also tried decreasing the time step by 2 (dtFactor = 0.5) and turning
off the pressure and velocity interpolation onto the new mesh, neither of which
had any significant effect on the total run time before the models stopped
converging. In all of the cases above I used the MUMPS solver, which
performed better than the default solver.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>The convergence issue is also not likely related to the specific upper
crustal yielding rheology, as I've tried both DruckerPrager, VonMises and the
yielding law used in the Wijns et al. models.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Finally, I tried using a free-slip top boundary with a weak,
low-density layer above the upper crust, but this produced a whole different
set of issues.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Thanks in advance to anyone who has some ideas/input on the convergence
issues and I've attached a sample input file (resolution = 0.5 km, ppc = 60) if
that helps at all.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Cheers,<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>John Naliboff<o:p></o:p></span></font></p>
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