[aspect-devel] Onset of convection, time step choice

[Max Rudolph]

Gerry,
Yes, that is exactly how I told my students to set up the problem. The only
change from cookbooks/convection-box.prm that we made is to use dimensional
parameters and change the aspect ratio. I put one possible solution here on
our course website, which uses bisection to determine the critical rayleigh
number for a given aspect ratio. It's kind of an ugly solution in that it
uses MATLAB to generate aspect input files and call aspect, but this is the
general approach that I suggested to my students. I only run ASPECT for one
timestep. If the rms velocity increases between time step 0 and time step
1, I assume that perturbations are growing. Otherwise they are decaying.
The code plots the growth rate and a line indicating the numerical result
and the result from the linear stability analysis and prints the error
(2-norm) in the command window.

http://web.pdx.edu/~rmaxwell/teaching/G610_Geodynamic_Modeling/m_files/racr/

If you might be interested in adapting this in some way as a more polished
teaching demo, let's follow up off the mailing list!

Cheers
Max

On Sat, Oct 8, 2016 at 2:44 PM, Elbridge Gerry Puckett <
egpuckett at ucdavis.edu> wrote:

> Hi Max,
>
> What you had your students do is a super!  I've been meaning to write a
> Cook Book that would allow one to do this in a fashion that would follow
> the linear stability analysis
>
> 6.19 Linear Stability Analysis for the Onset of Thermal Convection in a
> Layer of Fluid Heated from Below
>
> on pages 312-316 of the
>
> Third Edition of Turcotte and Schubert's book 'Geodynamics'
>
>  I believe the current first Cook Book parameter file is actually Cases
> (1a) - 1(c) of the Blankenbach Benchmark
>
> "A benchmark comparison for mantle convection codes" Geophys. J . Int.
> (1989) 98, 23-38
>
> Harsha Lokavarapu and I worked up a parameter file that gives the (two
> subdomain) counter-rotating flow that is illustrated at the top of page 312
> of Turcotte and Schubert. The only change in our parameter file from the
> analysis in the book is that our initial temperature perturbation is not
> identical to the one Turcotte uses in his analysis (bottom of p. 312).
> That is because his perturbation seems to take too long to produce the
> counter-rotating flow. See Issue
>
> https://github.com/geodynamics/aspect/issues/1027
>
> which was opened during the last ASPECT hackathon.  You might also look at
>
> https://github.com/geodynamics/aspect/issues/1128
>
>
> the reason this project has stalled is that I have never taught a class on
> this material and I generally develop these sort of teaching materials when
> I'm teaching the subject.  (At least that's one excuse! :-))
>
> would you like to collaborate on this, since you've just taught this
> material and, I assume, have asked your students to find the minimum of the
> curve on page 315 of Turcotte and Schubert.
>
> Best Wishes,
>
> - Gerry
>
>
>
> On 10/07/2016 03:36 PM, Max Rudolph wrote:
>
> Dear All,
> I am teaching geodynamic modeling this term, and asked my students as an
> introductory assignment to try to use ASPECT to determine experimentally
> the critical Rayleigh number for the onset of convection for an isoviscous
> fluid, heated from below with free-slip boundary conditions. The students
> did this by modifying cookbooks/convection-box.prm. One student found that
> convection began at Ra less then half the critical Ra for the chosen aspect
> ratio of 4:3. Of course, it turned out that too large a timestep was
> allowed. If the timestep size is limited to, say 100 Myr, we recover the
> correct value of Ra_{cr} within ~5% even for relatively coarse meshes
> (refinement level 4). I was a bit surprised, however, that the default
> timestep taken by ASPECT was so large. In fact, we had convergence problems
> for higher refinement levels for the default maximum timestep. For a
> problem like the one that we were running, a reasonable maximum timestep
> seems to be L^2/kappa (thermal diffusion timescale), where L is a
> characteristic length scale for the domain. Does it seem reasonable to
> change the way that ASPECT computes the maximum time step based on this
> idea rather than using 10^300 (the current default value, which seems
> entirely arbitrary)? I am happy to submit a pull request to do this, but
> don't want to waste my time if it's unlikely to be accepted.
>
> Cheers
> Max
>
>
>
>
>
> _______________________________________________
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>
>
>
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