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projection method, commutator error

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Old   September 28, 2015, 02:20
Default projection method, commutator error
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adam
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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
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Old   September 28, 2015, 04:11
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Filippo Maria Denaro
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Quote:
Originally Posted by adamphy View Post
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
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Old   September 28, 2015, 11:38
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Quote:
Originally Posted by FMDenaro View Post
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,

Thanks a lot for your answer.
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