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

[John Naliboff]

Hi Walter,

Yep, the stress values make a lot more sense now that I've added the pressure back in.

So in general, would it be reasonable to say that the sum of the deviatoric stress values is a good indicator how large the compressibility term is (i.e. since the deviatoric stress tensor trace should sum to zero)?  I checked and in some models this non-zero value is quite small (>4 orders of magnitude smaller than non-hydrostatic stresses), while in others it is larger (1 or 2 orders of magnitude smaller than non-hydrostatic stresses).

Also, what are some of the analytical solutions you tested for the side stress boundary conditions?  The few tests I've tried behaved reasonably well, but I'd definitely like to also try out some of the scenarios that don't give good matches to the analytical solutions.

Thanks again,
John


On Jul 31, 2010, at 12:07 PM, Walter Landry wrote:

> 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