[CIG-LONG] Convergence issues with long-term extension models

[Walter Landry]

Hi John,

Sorry it took a while to get back to you.

John Naliboff <jbnaliboff at ucdavis.edu> wrote:
> Hello all,
> 
> I'm hoping to get some input on convergence problems I'm having with
> 2D long-term extension models.
> 
> 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).

I think it may be because the hydrostatic term you are using assumes
that the density profile stays more or less constant through time.  In
your case, the whole region gets thinner as the material extends, so
the StressBC is trying to pull up the material.  But the StressBC can
not, because the bottom boundary does not move vertically.  This can,
unfortunately, cause a numerical instability.

Since you have a prescribed horizontal velocity, the easiest way to
solve this is to have the bottom move up as the material thins.  Then
the StressBC will not be trying to pull as much on an immovable
object.  Getting it to compensate exactly is not needed.  An
approximate solution will work.

This is implemented in input/examples/tibet.xml.  I have implemented
it in your input file (see attached, it is a one line change), and it
seems to work better.

Cheers,
Walter Landry
walter at geodynamics.org
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