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Crank Nicolson scheme

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Old   December 12, 2006, 23:36
Default This question has been asked i
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Srinath Madhavan (a.k.a pUl|)
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This question has been asked in the past, however nobody has responded to it. I would appreciate if someone could help in this regard.

Why does the Courant number < 1 condition need to be respected if one uses pure Crank Nicolson (i.e. blending coefficient = 1 in OpenFOAM).

Crank Nicolson is a second-order implicit scheme. Based on Von Neumann stability analysis, it should be possible to march in time using larger time-steps if one respects the condition below:



Can someone explain? Am I wrong here??
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Old   December 13, 2006, 17:04
Default I am no expert but I think it
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Billy
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I am no expert but I think it is because of PISO. Although, Crank Nicolson is stable, the PISO algorithm requires a good initial guess in each iteration to be stable.
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Old   December 14, 2006, 04:47
Default Hy Msrinath80, I am no expe
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Jens Klostermann
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Hy Msrinath80,

I am no expert either, but in a German Textbook ("Numerik im Maschinenbau" by Schäfer) it says "...there can be stability problems with Crank Nicholson ist the solution of the problem is not smooth in space..." with further reference to the book of Hirsch.

Hop it helps

Jens
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Old   December 14, 2006, 10:29
Default Thanks Billy and Jens.
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Srinath Madhavan (a.k.a pUl|)
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Thanks Billy and Jens.
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Old   April 2, 2007, 10:16
Default Hello everybody, I want to us
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Hello everybody,
I want to use the Crank-Nicholson scheme for my calculations.
For using it, do I just have to enter the keyword "CrankNicholson" in the dictionary "fvSchemes"?
Or do I have to implement a mixing of fvm and fvc terms in the equation I want to solve, as written on page 43 of the programmers guide?
In the programmers guide they say:
solve
(
fvm::ddt(phi)
==
kappa*0.5*(fvm::laplacian(phi) + fvc::laplacian(phi))
)

Thanks in advance,
Ralph
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Old   April 9, 2009, 17:08
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Hello everybody;
Crank nicolson method is an implicit method.So we solve this harder than explicit methods.Also crank nickolson is second order accurate.To me, it is right choice.
I want to make a program of this method.I know its theory.But when ı want to write codes, ı cannot make easily.I need some tutorials or programs(Matlab language).Where can ı find these?...
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Old   November 14, 2010, 14:59
Default doubt on crankNicholson scheme
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Aldo Iannetti
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Hi,
Can anyone show me the cranckNicholsonDdtScheme.C lines where the blending with the Euler implicit happens?
thanks
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