On 06/14/2017 04:34 PM, Jaekwang Kim wrote:
I've read some articles that the governing equation (advection +
diffusion) is unstable when it has large Peclet number.
(Even though it has diffusion term.)
What I am concerning is that it is how to imply SUPG stabilization
method in deal.ii., because my future problem will include
advection-diffusion term....
In SUPG, people are considering residual term*( b dot nabla - c nabla^2
u -f )*
.. and I thought this is very closely related to step-9 formation.
But I am not still sure to assemble residual term in my weak form...
Jaekwang,
it is correct that you do need the stabilization (SUPG or whatever else
you want to use) for the advection as long as advection dominates
diffusion -- i.e., as long as the *local Peclet* number is large.
I am certain that there are many examples in the literature where you
can see this, but my intuition would be that you write down the usual
SUPG scheme for the advection terms, and then you just add the diffusion
term (without any modification) to the resulting bilinear form. I.e.,
the SUPG stabilization does not see and does not know about the
diffusion term.
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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