[CIG-LONG] Questions about Non-Newtonian Rheology

[Walter Landry]

Brian Wilson <bjwilson83 at gmail.com> wrote:
> Hi all,
> 
> I have a few questions about the power law creep example in the Gale user
> manual and non-Newtonian rheology in general in Gale. I'm new to this list
> so I apologize if these questions have been answered elsewhere; if so could
> someone please point me in the right direction?
> 
> 1)  What is the strain rate invariant in Gale? Largest eigenvalue? Trace?

The second invariant of the strain rate tensor.  The trace is 0 since
this is incompressible flow.

> 2) In the example, n is obviously the power, but what do A and T_0
> represent? What is the constitutive equation here?
> 
> 3) Assuming the constitutive equation is of the form "stress = k * |strain
> rate|^(n-1) * strain rate", where k measures the consistency of the fluid,
> for shear thinning or thickening fluids (this is what I have found in the
> literature), what norm is used for the strain rate? The invariant? In this
> case does Gale start with an initial guess for the strain rate inside the
> norm and then iterate until the strain rate converges?

There is a discussion of the equations in section A.5.2.4.
Unfortunately there is no link from the cookbook example to that
section, so I just added it.  Let me know if A.5.2.4 is confusing.

Cheers,
Walter Landry
walter at geodynamics.org