CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

convective stiffness matrix for FEM

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   December 21, 2005, 09:10
Default convective stiffness matrix for FEM
  #1
Juergen Kertz
Guest
 
Posts: n/a
Hello!

After some more or less successful experiments I came to the "segregated" methods, which would finally meet my needs considering memory consumption.

For previous tries used only diffusive terms (e.g. penalty method), and the stiffness matrix is well done with:

Aij=mue*INTEGRAL{dNi/dx*dNj/dx + dNi/dy*dNj/dy}dOmega

where i and j are matrix indices.

However, as I tried to add the convective term, I found an additional k-index, and I do not know what to do with this. The meaning is not described in any paper I found.

Cij=INTEGRAL{wi*(Nk*uk*dNj/dx + Nk*vk*dNj/dy)}dOmega

I know that the uk and vk are taken from the previous iteration to avoid the nonlinearity,but I do not know where to put the k-index (if it even means an index) into the algorithm and my code.

For further explanation or my set-up: I want to calculate steady viscous flow (plastics extrusion die) in 2D (for the first try) with linear 3-node-triangle-elements.

Can somebody please tell me what the k's mean, or point me to a document where the matrix assembly algorithm is described?

Thank you!

Juergen
  Reply With Quote

Old   December 21, 2005, 16:54
Default Re: convective stiffness matrix for FEM
  #2
Renato.
Guest
 
Posts: n/a
Hi Juergen,

take a look in page 21 of http://www.nacad.ufrj.br/~rnelias/El...._Tese_Msc.pdf

Although written in portuguese, I think it can help you...

Cheers

Renato.
  Reply With Quote

Old   December 22, 2005, 03:03
Default Re: convective stiffness matrix for FEM
  #3
Rami
Guest
 
Posts: n/a
Juergen,

According to the Einstein convention a repeated index means summation. Therefore k is a dummy index to be summed on the relevant range (probably k=1,2,3 for 3D).

I hope this helps,

Rami

  Reply With Quote

Old   December 22, 2005, 03:07
Default Re: convective stiffness matrix for FEM
  #4
Juergen Kertz
Guest
 
Posts: n/a
Hi Renato,

Thank you very much for that document! This is a very good work! The things are described "for the programmer", and this is what I needed. I think I can handle my problem with this now, I will try today.

Did you ever think of translating your work (it is your work, isn't it?) to english (or even better german)? I think A LOT of people could use it very well!! As far as I could read the titles with my little italian knowledge, you describe highly sophiticated concepts in an easy-to-read way.

Thanks again!

Juergen
  Reply With Quote

Old   December 22, 2005, 04:22
Default Re: convective stiffness matrix for FEM
  #5
Juergen Kertz
Guest
 
Posts: n/a
Thank you Rami for you answer!

This is exactly what Renato's document says (which I'm trying to read just in this moment)

Looking at my problem with this knowledge makes my further work much easier! In fact, I feel the answer is so obvious, I must be some kind of stupid that I didn't get it on my own.

Thanks,

Juergen
  Reply With Quote

Old   December 23, 2005, 06:55
Default Re: convective stiffness matrix for FEM
  #6
Renato.
Guest
 
Posts: n/a
Hi Juergen,

When I was stating my CFD studies I had the same kind of doubt about Einstein's notation and after that, I decided to write all FEM matrices to incompressible flow in my MSc's dissertation.

Regarding the translation: unfortunately, here in Brazil, we're not encouraged to write our dissertations and thesis in any other language rather than Portuguese. We only publish articles in English. In fact, most of the Brazilians don't need to know a second language. We are a huge country where everybody speak Portuguese, besides being surrounded by Latin countries.

It brings me to a curiosity: "How many north Americans learn a second language? Maybe Spanish... They are also a huge country speaking an international language" Lucky guys...

Regards and Merry Christmas

Renato.

  Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Force can not converge colopolo CFX 13 October 4, 2011 22:03
Efficient Conversion of Local Stiffness Matrix to Global Stiffness nlane Main CFD Forum 2 September 14, 2010 18:26
Extracted stiffness matrix (K) !? mechanicaldesign ANSYS 0 January 22, 2010 05:04
OpenFOAM version 1.6 details lakeat OpenFOAM Running, Solving & CFD 42 August 26, 2009 21:47
stiffness matrix happy_clp Main CFD Forum 0 March 25, 2009 04:31


All times are GMT -4. The time now is 11:03.