# projection method, commutator error

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

 September 28, 2015, 02:20 projection method, commutator error #1 New Member   adam Join Date: Sep 2015 Posts: 2 Rep Power: 0 Dear Community, I'm studying projection methods. I saw some papers mentioned some second order methods (e.g., J. B. Bell, P. Colella, and H. M. Glaz. J. Comp. Phys., 85(2):257{283, 1989) have commutator error if boundary condition is not periodic, because the projection operator and the laplacian don't commute. 1. Does Bell etal's method still have commutator error on staggered grid? 2. Does this error decreases with time step size? 3. Is Chorin's first order method (on staggered grid) also have this kind commutator error? 4. Can anyone recommend some paper talking about this kind of error? Thanks in advance. Adam Last edited by adamphy; September 28, 2015 at 02:31. Reason: add details

September 28, 2015, 04:11
#2
Senior Member

Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,259
Rep Power: 67
Quote:
 Originally Posted by adamphy Dear Community, I'm studying projection methods. I saw some papers mentioned some second order methods (e.g., J. B. Bell, P. Colella, and H. M. Glaz. J. Comp. Phys., 85(2):257{283, 1989) have commutator error if boundary condition is not periodic, because the projection operator and the laplacian don't commute. 1. Does Bell etal's method still have commutator error on staggered grid? 2. Does this error decreases with time step size? 3. Is Chorin's first order method (on staggered grid) also have this kind commutator error? 4. Can anyone recommend some paper talking about this kind of error? Thanks in advance. Adam

The commutator error does not depend on the type of grid, it is a more general "mathematical" issue.
Some years ago I published a couple of paper that analyzed these topics, you can find them on IJNMF

September 28, 2015, 11:38
#3
New Member

Join Date: Sep 2015
Posts: 2
Rep Power: 0
Quote:
 Originally Posted by FMDenaro The commutator error does not depend on the type of grid, it is a more general "mathematical" issue. Some years ago I published a couple of paper that analyzed these topics, you can find them on IJNMF
Dear Prof. Denaro,

 Tags commutator error, projection method, staggered grid