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

non-linear terms in conservative or non-conservative form

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

Like Tree5Likes
  • 1 Post By FMDenaro
  • 1 Post By FMDenaro
  • 1 Post By cfdnewbie
  • 1 Post By FMDenaro
  • 1 Post By praveen

Reply
 
LinkBack Thread Tools Display Modes
Old   May 24, 2012, 06:56
Unhappy non-linear terms in conservative or non-conservative form
  #1
Member
 
Join Date: Jun 2010
Posts: 98
Rep Power: 7
Hooman is on a distinguished road
Hi,

When solving an equation that involves non-linear terms such as u\frac{\partial u}{\partial x} in Burger's equations. Will the results be different if the conservative form of the term \frac{1}{2}\frac{\partial u^{2}}{\partial x} was used instead. Does it result in differences in terms of accuracy and stability.

Thanks!
Hooman is offline   Reply With Quote

Old   May 24, 2012, 11:28
Default
  #2
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,587
Rep Power: 20
FMDenaro will become famous soon enough
Quote:
Originally Posted by Hooman View Post
Hi,

When solving an equation that involves non-linear terms such as u\frac{\partial u}{\partial x} in Burger's equations. Will the results be different if the conservative form of the term \frac{1}{2}\frac{\partial u^{2}}{\partial x} was used instead. Does it result in differences in terms of accuracy and stability.

Thanks!
yes, the discrete equations can drive to very different results (e.g. different wave propagation), as advice you must use always the conservative form!
Hooman likes this.
FMDenaro is offline   Reply With Quote

Old   May 24, 2012, 11:39
Default
  #3
Member
 
Join Date: Jun 2010
Posts: 98
Rep Power: 7
Hooman is on a distinguished road
Thanks very much.

On a slightly different note, if the non-lineaity was in an unsteady term for instance \frac{\partial}{\partial t}\left(v^{2}\right), how would one go about discretizing with respect to time? Say, Explicit Euler was being used, would it be possible to just find v^2 at the next time step and take the square root of that or is there more to it due to the non-linearity? I think this would reduce the accuracy but I am not really sure.

Thanks again!
Hooman is offline   Reply With Quote

Old   May 24, 2012, 11:46
Default
  #4
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,587
Rep Power: 20
FMDenaro will become famous soon enough
Quote:
Originally Posted by Hooman View Post
Thanks very much.

On a slightly different note, if the non-lineaity was in an unsteady term for instance \frac{\partial}{\partial t}\left(v^{2}\right), how would one go about discretizing with respect to time? Say, Explicit Euler was being used, would it be possible to just find v^2 at the next time step and take the square root of that or is there more to it due to the non-linearity? I think this would reduce the accuracy but I am not really sure.

Thanks again!
The equation for the kinetic energy equation has such a term and the equation is solved in time for the variable k=u^2 ....
Hooman likes this.
FMDenaro is offline   Reply With Quote

Old   May 24, 2012, 13:51
Default
  #5
Senior Member
 
cfdnewbie
Join Date: Mar 2010
Posts: 551
Rep Power: 11
cfdnewbie is on a distinguished road
Just as a quick addition to this: There's something called the "skew symmetric form" that avoids aliasing errors and consists of a combination of both formulations. In that sense, it might not always be advisable to use the conservative form alone, but on general, yes, use it rather than the non-con form!
Hooman likes this.
cfdnewbie is offline   Reply With Quote

Old   May 31, 2012, 12:37
Default
  #6
Member
 
Join Date: Jun 2010
Posts: 98
Rep Power: 7
Hooman is on a distinguished road
Thanks!

Can I just ask more specifically why the conservative form is preferred. If you know any good reading material on this specific topic , please let me know.
Hooman is offline   Reply With Quote

Old   May 31, 2012, 12:59
Default
  #7
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,587
Rep Power: 20
FMDenaro will become famous soon enough
Quote:
Originally Posted by Hooman View Post
Thanks!

Can I just ask more specifically why the conservative form is preferred. If you know any good reading material on this specific topic , please let me know.
any CFD book treating the FV approach is good for you, e.g. LeVeque, Ferziger & Peric, etc ...
then, many papers in journals are more specific in analyzing the properties of the conservative (divetgence) form in terms of accuracy and stability
Hooman likes this.
FMDenaro is offline   Reply With Quote

Old   June 1, 2012, 00:20
Default
  #8
Super Moderator
 
praveen's Avatar
 
Praveen. C
Join Date: Mar 2009
Location: Bangalore
Posts: 244
Blog Entries: 6
Rep Power: 9
praveen is on a distinguished road
If solutions are discontinuous, then conservative form should be used.

For smooth solutions, the skew symmetric form can be used; it conserves energy and thats one of the reasons it is used.
Hooman likes this.
praveen is offline   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
Rewriting twoPhaseEulerFoam in conservative form alberto OpenFOAM Running, Solving & CFD 26 May 26, 2015 03:05
Conservative form of Navier Stokes equation. balkrishna OpenFOAM Running, Solving & CFD 2 January 25, 2012 09:33
Conservative form bardiche Main CFD Forum 0 February 9, 2011 20:58
solution diverges when linear upwind interpolation scheme is used subash OpenFOAM 0 May 29, 2010 01:23
conservative, non conservative form???? vijesh joshi Main CFD Forum 4 March 16, 2006 00:10


All times are GMT -4. The time now is 23:56.