[CIG-LONG] Hydrostatic Pressure and linear side stress boundary conditions

[Walter Landry]

Karen Paczkowski <karen.paczkowski at yale.edu> wrote:
> I am a graduate student at Yale University.  I am trying to model a
> subduction zone, where the mantle passively responds to the slab
> movement.  To do this I would like to specify some shapes where within
> these I set velocities to represent the slab, but then only specify
> stresses as the boundary conditions on the larger simulation domain.
> So I like to just have the bottom, side and top boundary conditions be
> the equilibrium stress conditions of the system so that the flow field
> in the mantle will just organize itself naturally as a passive
> response to the subducting slab's movement.
> 
> I thought this would mean that I should specify:
> 1) the bottom boundary condition as a stress acting up (in the y
> direction) equal to the stress from the force of gravity acting down
> 2)  the top boundary condition would just be the hydrostatic term
> 3) the side boundary condition would be a linear gradient going from
> the value at the bottom to that at the top.

The hydrostatic terms are subtracted out of the equations, so that
changes what kind of boundary conditions you need to apply.  Before
subtracting out the hydrostatic terms, you would need to apply
hydrostatic stresses at the bottom and sides, but not at the top.
After subtracting out the hydrostatic terms, it is reversed.  You do
not need to do anything special on the bottom or sides, but you need a
special stress on the top.

Unfortunately, with that setup the code will not run.  The Stokes
equations need a velocity condition somewhere in the simulation.  You
will have that once you add the subducting slab.

So I am attaching a new version of your input file.  I fix the
velocities of the left side of the simulation, but not the right.  So
material should be able to flow out the right side.

Also, I set the density of the material to be a little larger than the
hydrostatic term.  Otherwise, all of the forces are zero and Gale will
not take a single step.

One thing to note is that it is easy to run into the Drunken Seaman
problem with this setup.  So I set dtFactor=0.1.

Let me know if you have any more questions.

Cheers,
Walter Landry
walter at geodynamics.org
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