[CIG-MC] SUPG method in CitcomS

[Jed Brown]

On Sat, Apr 7, 2012 at 08:35, Matthew Knepley <knepley at mcs.anl.gov> wrote:

> It will get rid of oscillation and conserve the quantity (looks a little
> like FCT), but the 0,1 bounds make no sense to me
> for energy. For concentration (as in the paper), they are natural.
>

FCT is still locally conservative. The superbee limiter has some sharpening
ability, but not as much as Lenardic's filter. The filter is more like
volume of fluid interface reconstruction, but without the defined normals
and precise interface location of a scheme like PLIC.

http://math.uh.edu/~caboussat/Work/Papers/Files/caboussat_arcme.pdf

The closest analogue that would work for temperature is probably clipping
with global compensation, but that is very likely to change the dynamics of
the system. Also note that this clipping is not random redistribution of
mass/energy; depending on the advection scheme, the oscillations can lead,
be centered on, or trail the intended discontinuity, leading to systematic
mass/energy channels. This may explain why Paul's paper showed such highly
different dynamics with and without the filter.

I believe that for energy, you want a locally conservative non-oscillatory
method. Clipping is a delicate world to get into. If you have strict max
and/or min bounds and want higher than second order accuracy, there are
more principled limiting techniques that can preserve the high order
accuracy and local conservation (e.g. Zhang and Shu's positivity-preserving
limiters; note that these change the definition of max/min to be in terms
of the reconstructed initial state instead of the piecewise averages for
which a very simple argument shows that any max/min preserving method
cannot be more than second order accurate).
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://geodynamics.org/pipermail/cig-mc/attachments/20120407/2cb9f84c/attachment.htm