[aspect-devel] Problems with periodic boundary conditions

[Ian Rose]

Hi Max,

I suspect that you are running afoul of the nullspace in your problem.  I
played with the parameter file a bit, and the solver failures seem to be
very dependent on mesh resolution, refinements, and domain geometry (though
not Ra directly, as far as I can tell).

The periodic box with free slip boundaries has the compatibility condition

\int_V \rho g_x = 0

Of course, a vertical gravity field should satisfy this automatically, but
it might be the case that roundoff errors could cause problems.  I still
suspect the nullspace because I can make the crashes go a way by (a)
reducing the solver tolerance or (b) making one of the boundaries no slip.
What do others think, am I completely off base?  If this is the problem,
what would be the best way to address it?

Ian


On Wed, Nov 5, 2014 at 8:58 PM, Max Rudolph <maxwellr at gmail.com> wrote:

> Dear All,
> I'm trying to set up a simple 2D calculation (in a box) with periodic
> boundary conditions. I keep running into the error message below
> (about numerical breakdown). A solution is obtained for the first
> timestep (0) but for the second timestep the 'numerical breakdown'
> error appears. It seems that this error is related to Ra - aspect runs
> fine for the low-Ra case but when I increase the layer depth so that
> Ra~10^8, there are errors. I tried re-meshing every timestep and
> reducing the CFL number to 0.01 to no avail. Is this a known problem?
> Either way, do you have any suggestions about how to work around this?
>
> Thanks!
> Max
>
> ----------------------------------------------------
> Exception on processing:
>
> --------------------------------------------------------
> An error occurred in line <246> of file
> </opt/deal.II-8.1-src/source/lac/trilinos_solver.cc> in function
>     void dealii::TrilinosWrappers::SolverBase::execute_solve(const
> dealii::TrilinosWrappers::PreconditionBase &)
> The violated condition was:
>     false
> The name and call sequence of the exception was:
>     ExcMessage("AztecOO::Iterate error code -2: " "numerical breakdown")
> Additional Information:
> AztecOO::Iterate error code -2: numerical breakdown
> --------------------------------------------------------
>
> Aborting!
> ----------------------------------------------------
>
> input file used (left file is my modified input file, right file is
> cookbook.
>
> max at harding:~/aspect_runs$ diff periodic_box.prm
> /opt/aspect-dev/cookbooks/future/periodic_box.prm
> 2c2
> < set CFL number                             = 0.01
> ---
> > set CFL number                             = 1.0
> 4c4
> < set Output directory                       = output_pb
> ---
> > set Output directory                       = output
> 39,41c39,41
> <     set X extent = 4.2e6
> <     set Y extent = 3.0e6
> < #    set Z extent = 5.e5
> ---
> >     set X extent = 1.e6
> >     set Y extent = 5.e5
> >     set Z extent = 5.e5
> 58,60c58
> <     set Function constants = Ttop=0.0, Tbottom=1000.0, p=0.01,
> H=3.0E6, W=4.2e6, pi=3.1415926
> <     set Function expression = Tbottom - (Tbottom-Ttop)*y/H +
> p*sin(pi*y/H)*cos(2.0*pi*x/W)
> <
> ---
> >     set Function expression = if((sqrt((x-1.e5)^2+(y-4.0e5)^2)<5.0e4) |
> (sqrt((x-3.e5)^2+(y-2.e5)^2)<1.0e5) , 800.0, 0)
> 85c83
> <   set Time steps between mesh refinement = 1                       #
> default: 10
> ---
> >   set Time steps between mesh refinement = 10                       #
> default: 10
> 100c98
> <   set List of postprocessors = velocity statistics, visualization,
> temperature statistics, heat flux statistics, basic statistics
> ---
> >   set List of postprocessors = visualization
> 104,105c102,103
> <     set Output format                 = hdf5
> <     set Time between graphical output = 0.0
> ---
> >     set Output format                 = vtu
> >     set Time between graphical output = 1.e3
> max at harding:~/aspect_runs$
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