
[Sponsors] 
May 20, 2012, 05:28 
can a limiter be eliminated

#1 
New Member
Moon Chen
Join Date: May 2012
Posts: 7
Rep Power: 6 
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!


May 20, 2012, 07:02 

#2  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,518
Rep Power: 31 
Quote:


May 20, 2012, 09:25 
can a limiter be eliminated?

#3  
New Member
Moon Chen
Join Date: May 2012
Posts: 7
Rep Power: 6 
Quote:
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! 

May 20, 2012, 11:09 

#4  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,518
Rep Power: 31 
Quote:
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. 

May 31, 2012, 23:15 

#5  
New Member
Moon Chen
Join Date: May 2012
Posts: 7
Rep Power: 6 
Quote:


June 1, 2012, 03:59 

#6 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,518
Rep Power: 31 

June 1, 2012, 05:45 

#7 
Super Moderator

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 NavierStokes), then solutions will be smooth though the gradients might be large in some regions. Then with enough grid adaptation, you can get nonoscillatory solutions without limiters. 

June 1, 2012, 06:01 

#8  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,518
Rep Power: 31 
Quote:


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Ultimate Flux Limiter  gentela  Main CFD Forum  1  August 2, 2016 20:55 
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 
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 