[CIG-LONG] Gale stress tensor verse pressure output in .dat and vtk files

[Walter Landry]

John Naliboff <jbnaliboff at ucdavis.edu> wrote:
> Hi Walter,
> 
> I have a number of questions regarding the Gale stress tensor and pressure output values in the .dat and vtk files.
> 
> Specifically, I've been doing tests with side stress boundary conditions

I have never gotten side stress boundary conditions to work well.  I
always had problems with the numerical solution being far too
different from the analytic solution.  However, with a HydrostaticTerm
component, the hydrostatic term is already subtracted out, so that
might work.

> and in doing so I noticed that there seems to be a discrepancy
> between the stress tensor values and the magnitude/value of the
> pressure.

> My interpretation of the pressure is (sigma_xx + sigma_yy)/2 in 2D
> or (sigma_xx + sigma_yy + sigma_zz)/3 in 3D.

The stress that is output is mostly the deviatoric stress.  Because of
the numerical compressibility term, it will not be completely
deviatoric.  To get the true pressure you would then add the trace of
the stress to the pressure-like variable.

In practice, if the compressibility term gets significant, then you no
longer have something that is close to incompressible.  So you would
need to throw out the whole solution anyway.

Cheers,
Walter Landry
walter at geodynamics.org