Re: [Libmesh-users] space varying dt for time stepping

[Roy S. <roy...@ic...>]

On Wed, 24 Apr 2013, Manav Bhatia wrote:

>   Has anyone attempted space varying dt for time stepping problems using
> libMesh?

No, but we've got an application where it might be a decent idea.

Half-ignorant rant:

I'm skeptical, though.  Space varying dt is ideal if you're doing a
time-accurate solve of a hyperbolic problem, or if you can do
operator-splitting and limit the space varying dt to the explicit
operator(s) in a parabolic problem, but I've never seen how you can do
implicit space-varying dt in a time-accurate way on parabolic problems
without adding more DoFs to each space-time slab and so canceling out
most of your benefits.

What other implicit hypersonics people do with space-varying dt seems
to be limiting it to non-time-accurate solves, where you're just
pseudo time stepping to get to a quasi steady state.  Which is fine,
we do pseudo time stepping too... except that I think the right thing
in this case may be to go coarser in time *and* space; if you're
basically using the non-time-accurate parts of your solve just to get
the shock moved into place so you can use larger dt, you might as well
do most of that movement on a coarse grid.
---
Roy