[petsc-users] Using DM for a refined level-set grid

Jed Brown jed at jedbrown.org
Fri Feb 21 18:50:48 CST 2014

Åsmund Ervik <asmund.ervik at ntnu.no> writes:

> We're talking about adding a refined level-set grid method
> (M. Herrmann, doi:10.1016/j.jcp.2007.11.002) to our code. Currently we
> solve two-phase Navier-Stokes (ghost fluid method) together with a
> standard level-set approach on a uniform Cartesian grid.
> What we're thinking is the following: we will have 2 grids for the
> level-set function. One will be the same as for the flow field, this
> is the coarse grid. The other is a refined (still uniform Cartesian)
> grid used only for the level-set function. The coarse grid will have
> values that lets us know if we are close to an interface or not. If we
> are not close to an interface, we don't want to store (allocate) any
> value for the level-set function on the fine grid. I'm guessing
> "close" will mean roughly "when the absolute value of the level-set
> function is <5*dxCoarse".

Is this 2D or 3D, what fraction of the domain is likely to be within
5*dxCoarse of the interface, and how large do you intend your subdomains
to be?

My worry is that even if you implement the dynamic algorithm you're
thinking of (which is nontrivial to do well), some subdomains will have
nearly-full refined sections which will limit your max problem size and
performance.  If you can't load balance dynamically (in terms of peak
memory and time) at the needed granularity, there is no point trying to
save some storage in benign regions of your domain.

What sort of methods will you be using for your CFD?  Does it involve
assembled matrices?
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