[aspect-devel] Some interesting (pathological?!) behaviour of particles ... Do we need CVI here?

[Wolfgang Bangerth]

Gerry,

> QUESTION: Where should I put the code to compute the convergence of the SolCx,
> SolKz and  SolVI (inclusion) benchmarks when active tracers carry the density
> and viscosity as in the Thielmann, May and Kaus?  I have thought of putting a
> benchmark directory in the source/particle directory, or in the benchmark
> folder or ...?  Any suggestions?  Wolfgang?

There is already a directory benchmark/solcx (and benchmark/solkz). Why not 
create parallel directories benchmark/solcx-particles and 
benchmark/solkz-particles?


> My fascination with this computation was the manner in which the dynamics of
> the particle paths, which is a dynamical system of the form
>
>     d/*x*/ (t) / dt = /*u*/(x(t), y(t), t)
>
>     /*x*/(0) = /*x*/_0
>
> where /*x*/ (t) is the trajectory of the particle that starts at  *x*_0 at t =
> 0, leads to a limit point (a black hole!) on the lower left, and a limit cycle
> to the right of it - the particle paths that look like an egg.  I think this
> is SO COOL!

I think that's quite neat. Mathematically, the divergence of the *numerical* 
solution is of course not zero, but it is zero in some average sense (when 
weighted by the pressure shape functions). That means in practice that it must 
be oscillatory, and that will create regions where the flow is divergent and 
others where it is divergent. I bet that this creates attractors such as seen 
for your particles.

When you go to finer and finer meshes, the "attracting valleys" get thinner 
and thinner (they're smaller than a cell since the oscillation of the 
divergence happens at the cell level) and so they become less and less visible 
the finer the mesh is.

Best
  W.

-- 
------------------------------------------------------------------------
Wolfgang Bangerth               email:            bangerth at math.tamu.edu
                                 www: http://www.math.tamu.edu/~bangerth/