[CIG-MC] SUPG method in CitcomS
shijie.zhong at Colorado.EDU
Fri Apr 6 18:19:27 PDT 2012
The oscillation is less for better resolution and smaller time step. However, I agree that if some better inexpensive scheme can be implemented, it would be super. Like Thorsten said, this item was on the wish list to CIG.
Shijie Zhong, Professor
Department of Physics
University of Colorado at Boulder
Boulder, CO 80309
Tel: 303-735-5095; Fax: 303-492-7935
From: cig-mc-bounces at geodynamics.org [cig-mc-bounces at geodynamics.org] On Behalf Of Thorsten Becker [thorstinski at gmail.com]
Sent: Friday, April 06, 2012 5:44 PM
To: Magali Billen
Cc: cig-mc at geodynamics.org
Subject: Re: [CIG-MC] SUPG method in CitcomS
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.
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  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...
> Associate Professor & Chancellor Fellow, U.C. Davis
> Chair, Geology Graduate Program
> Department of Geology & KeckCAVES
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