[CIG-MC] SUPG method in CitcomS

[Thorsten Becker]

Hi Magali 

I think you're spot on. Advection dominated problems suffer from those oscillations with the default method, and filtering or higher spatio-temporal  resolution are workarounds. For the most part, the oscillations are harmless if detected, and typically don't arise for convection problems (as opposed to the start a slab problems we all like). This iffiness is why we put "new energy solver" with semi Lagrangian as a guess on the wish list for CIG. 

Cheers

T  

Thorsten W Becker - USC

On Apr 6, 2012, at 15:49, 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).
> 
> 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...
> Magali
> 
> <gunzburger-stab3.pdf>
> 
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