[aspect-devel] cylindrical rigid body rotation

[Timo Heister]

> Great, thanks Timo!

and thanks, Ian! :-)

>> It is quite difficult to construct an example where those two methods
>> differ
>> by a lot.
>
> You'd need a model where the density is not nearly constant, for example a
> compressible one.

Sure, but that is not enough. For the Krylov method to converge, the
right-hand side needs to be compatible (be in the image of the
operator). This means we can only generate net rotation in the order
of the Krylov residual (so something like 1e-8), because GMRES will
stay in the nullspace we start with (and u=0 and t=0).
This explains why using adaptive mesh refinement produces non
negligible rotation quicker than a fixed mesh (it produces small
round-off).

So, I don't see a way to generate a significant difference in net
rotation and net angular momentum that is still compatible. Producing
a fake rotational component (for example a tangential gravity) means
that the linear solver won't converge (unless we make it compatible
which involves removing the rotational part again :-) ).

The only way I can see to create a significant difference is to
initialize our initial guess for the velocity with something with a
large rotational component (which is in the nullspace).

-- 
Timo Heister
http://www.math.clemson.edu/~heister/