[CIG-MC] SUPG method in CitcomS

[Matthew Knepley]

On Fri, Apr 6, 2012 at 5:49 PM, Magali Billen <mibillen at ucdavis.edu> wrote:

> Hello Shijie, Eh, and others...
>
> Following on the recent question on the list about max temperatures in
> CitcomS.
> I wanted to ask about the SUPG solver for the energy equation.
>
> My basic questions are:
>
> - Do you always expect to have some "small" temperature oscillation from
> the SUPG method?
> - If so, in your opinion when is it reasonable to use the Lenardic filter
> to prevent these small
> oscillations from growing?
> - If not, what strategy would you use to eliminate the temperature
> overshoots when decreasing
> the time-step doesn't eliminate them?
>
> For example, the slab benchmark in the manual gets temperature overshoots
> if you run that
> forward in time. Decreasing the time-step helps, but doesn't eliminate
> them.
>
> I've attempted to read some recent papers related to SUPG (after reading
> the earlier Brooks
> and Hughes papers), and I'm finding it difficult to understand the method
> well enough to know
> what its limitations are in non-steady-state problems (with or without
> strong flow gradients).
>

Amazingly, the first Google hit looks good:
http://rzbl04.biblio.etc.tu-bs.de:8080/docportal/servlets/MCRFileNodeServlet/DocPortal_derivate_00001549/Document.pdf

SUPG just introduces some diffusion in the streamline direction to prevent
oscillation. Its a little
goofy because you have the tune the amount of diffusion carefully. It does
not guarantee monotonicity.
The right thing to do is implement a monotonic method like TVD or WENO.
There are now easy, open
source implementations in http://numerics.kaust.edu.sa/pyclaw/. You can use
a low-pass filter (Lenardic)
to get rid of the oscillations, but the implications for accuracy are not
good and forget about conserving
anything.

I have said the simplest thing. Jed knows more about this.

    Matt