Re: [deal.II] Re: weak form for advection-diffusion equation

[Wolfgang Bangerth]

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.
--

Wolfgang Bangerth  email: bange...@colostate.edu
   www: http://www.math.colostate.edu/~bangerth/

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[deal.II] Re: weak form for advection-diffusion equation

[Jaekwang Kim]

Thanks for the response! 

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... 





2017년 6월 14일 수요일 오후 3시 40분 50초 UTC-5, Bruno Turcksin 님의 말:
>
> Jaekwang,
>
> in step-9 the test function is a little bit strange because if you use 
> continuous finite element to discretize the advection equation, the scheme 
> is unstable. So you basically add a diffusion term to the equation to 
> stabilize the scheme. However, your equation already has a diffusion term 
> so you may not need a stabilization term.
>
> Best,
>
> Bruno
>
> On Wednesday, June 14, 2017 at 3:33:18 PM UTC-4, Jaekwang Kim wrote:
>>
>>
>> 
>>
>>
>>

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[deal.II] Re: weak form for advection-diffusion equation

[Jaekwang Kim]

Adding up to this, I was trying as...


scratch_data.fe_values.shape_grad_grad (j,q_point)


but keep receiving errors 

*/Users/kimjaekwang/repos/advection_diffusion/step9/step-9.cc:487:53: **error: 
**no member named 'shape_grad_grad' in*

*  'dealii::FEValues<2, 2>'*

*   - scratch_data.fe_values.shape_grad_grad 
(j,q_point)*

point)



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