[CIG-MC] SUPG method in CitcomS

Magali Billen mibillen at ucdavis.edu
Fri Apr 6 15:49:49 PDT 2012

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).

From reading of one paper (Bochev et al., Stability of the SUPG FEM for transient advection-
diffusion problems, in Comput. Methods Appl. Mech Eng, v. 193, 2004, p 2301-2323), 
they point out that:
"Regarding the small localized oscillations in SUPG solutions we recall that SUPG is not monotonicity 
preserving, and that such oscillations can be expected in the vicinity of discontinuities and internal layers. 
Therefore, their presence cannot serve as an indication of a destabilization. Moreover, as the data in 
Tables 1–3 show, smaller time steps do not lead to an increase in the H1 seminorm of the solutions,
 i.e., these oscillations remain bounded for small time steps. An application of a discontinuity capturing 
operator [16] is recommended for a further suppression of these oscillations.

(I've attached the paper). This seems to indicate that one should expect these small oscillations where
there are rapid changes in flow, and that using something like the Lenardic filter is a reasonable thing
to do as long as your confident you have a good solution of the flow.

Any you advice or insight you have would be helpful...

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