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

can a limiter be eliminated

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

Reply
 
LinkBack Thread Tools Display Modes
Old   May 20, 2012, 05:28
Default can a limiter be eliminated
  #1
New Member
 
Moon Chen
Join Date: May 2012
Posts: 7
Rep Power: 5
moon_light is on a distinguished road
In order to suppress the oscillation, we cite a limiter resulting in avoiding the appearance of new extremum points. I am wondering can we add cells in the position of new extremum points but do not use a limiter. I hope in this way, we can obtain a more accurate simulation of discontinuous solution? Is there any existing techniques which associated with this method? Thank you!
moon_light is offline   Reply With Quote

Old   May 20, 2012, 07:02
Default
  #2
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,651
Rep Power: 23
FMDenaro will become famous soon enough
Quote:
Originally Posted by moon_light View Post
In order to suppress the oscillation, we cite a limiter resulting in avoiding the appearance of new extremum points. I am wondering can we add cells in the position of new extremum points but do not use a limiter. I hope in this way, we can obtain a more accurate simulation of discontinuous solution? Is there any existing techniques which associated with this method? Thank you!
You can use an adaptive refinement, in any case the presence of numerical oscillations must be controlled by a suitable scheme (e.g., ENO/WENO)
FMDenaro is offline   Reply With Quote

Old   May 20, 2012, 09:25
Default can a limiter be eliminated?
  #3
New Member
 
Moon Chen
Join Date: May 2012
Posts: 7
Rep Power: 5
moon_light is on a distinguished road
Quote:
Originally Posted by FMDenaro View Post
You can use an adaptive refinement, in any case the presence of numerical oscillations must be controlled by a suitable scheme (e.g., ENO/WENO)
When you say the adaptive refinement, are you referring to the moving mesh?
Generally speaking, the width of a discontinue part like a shock, is very small(less than the width of a grid), right?
I am wondering is there any algorithm which can find out the discontinue part automatically and then use low order schemes like two order scheme (linear TVD scheme) scheme but at the same time densify the grids to the extent that the scheme is TVD scheme and the accuracy requirements can be satisfied? Thank you!
moon_light is offline   Reply With Quote

Old   May 20, 2012, 11:09
Default
  #4
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,651
Rep Power: 23
FMDenaro will become famous soon enough
Quote:
Originally Posted by moon_light View Post
When you say the adaptive refinement, are you referring to the moving mesh?
Generally speaking, the width of a discontinue part like a shock, is very small(less than the width of a grid), right?
I am wondering is there any algorithm which can find out the discontinue part automatically and then use low order schemes like two order scheme (linear TVD scheme) scheme but at the same time densify the grids to the extent that the scheme is TVD scheme and the accuracy requirements can be satisfied? Thank you!

no, not a moving mesh but a local adaptive mesh based on the gradients threshold ...shock capturing schemes are designed for getting the discontinuity on the computational grid but, as you stated, the shock wave for NS equations can be as small as some mean free path, therefore is practically unresolvable on a grid. You must accept tha the shock layer is spreaded on some cells...
I suggest reading also the book of LeVeque on FV methods for hyperbolic systems.
FMDenaro is offline   Reply With Quote

Old   May 31, 2012, 23:15
Default
  #5
New Member
 
Moon Chen
Join Date: May 2012
Posts: 7
Rep Power: 5
moon_light is on a distinguished road
Quote:
Originally Posted by FMDenaro View Post
no, not a moving mesh but a local adaptive mesh based on the gradients threshold ...shock capturing schemes are designed for getting the discontinuity on the computational grid but, as you stated, the shock wave for NS equations can be as small as some mean free path, therefore is practically unresolvable on a grid. You must accept tha the shock layer is spreaded on some cells...
I suggest reading also the book of LeVeque on FV methods for hyperbolic systems.
Thank you! are you refering this book Finite Volume Methods for Hyperbolic Problems?
moon_light is offline   Reply With Quote

Old   June 1, 2012, 03:59
Default
  #6
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,651
Rep Power: 23
FMDenaro will become famous soon enough
Quote:
Originally Posted by moon_light View Post
Thank you! are you refering this book Finite Volume Methods for Hyperbolic Problems?
yes, this one
FMDenaro is offline   Reply With Quote

Old   June 1, 2012, 05:45
Default
  #7
Super Moderator
 
praveen's Avatar
 
Praveen. C
Join Date: Mar 2009
Location: Bangalore
Posts: 251
Blog Entries: 6
Rep Power: 9
praveen is on a distinguished road
If you are using second or higher order scheme for a hyperbolic problem, and your solution has discontinuities, then limiter are absolutely necessary. Even if you adapt the mesh, oscillations cannot be eliminated.

But if your problem is parabolic (like Navier-Stokes), then solutions will be smooth though the gradients might be large in some regions. Then with enough grid adaptation, you can get non-oscillatory solutions without limiters.
praveen is offline   Reply With Quote

Old   June 1, 2012, 06:01
Default
  #8
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,651
Rep Power: 23
FMDenaro will become famous soon enough
Quote:
Originally Posted by praveen View Post
If you are using second or higher order scheme for a hyperbolic problem, and your solution has discontinuities, then limiter are absolutely necessary. Even if you adapt the mesh, oscillations cannot be eliminated.

But if your problem is parabolic (like Navier-Stokes), then solutions will be smooth though the gradients might be large in some regions. Then with enough grid adaptation, you can get non-oscillatory solutions without limiters.
yes, a well know theorem states that monotone linear scheme can be only first order accurate. The key is to build a non-linear scheme (also for solving linear hyperbolic equations) and a limiter is a way to do that.. however, I suggest more modern schemes such as ENO/WENO reconstructions
FMDenaro 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
slope limiter of discontinuous Galerkin on triangular element(2D, P2 polynomial) effort8 Main CFD Forum 1 March 19, 2012 10:03
slope limiter and flux limiter ?? Ameya J Main CFD Forum 1 June 13, 2011 12:05
Ultimate Flux Limiter gentela Main CFD Forum 0 October 3, 2010 03:43
Definition of limiter function for central dirrerencing scheme sebastian_vogl OpenFOAM Running, Solving & CFD 0 January 5, 2009 12:08
Moment limiter in DG method. jinwon park Main CFD Forum 0 May 15, 2008 12:18


All times are GMT -4. The time now is 19:38.