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-   -   Crank Nicolson scheme (http://www.cfd-online.com/Forums/openfoam-solving/59758-crank-nicolson-scheme.html)

msrinath80 December 12, 2006 23:36

This question has been asked i
 
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:

http://www.cfd-online.com/OpenFOAM_D...your_image.gif

Can someone explain? Am I wrong here??

billy December 13, 2006 17:04

I am no expert but I think it
 
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.

jens_klostermann December 14, 2006 04:47

Hy Msrinath80, I am no expe
 
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

msrinath80 December 14, 2006 10:29

Thanks Billy and Jens.
 
Thanks Billy and Jens.

ralph April 2, 2007 11:16

Hello everybody, I want to us
 
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

student_58 April 9, 2009 18:08

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?...

aldo.iannetti November 14, 2010 14:59

doubt on crankNicholson scheme
 
Hi,
Can anyone show me the cranckNicholsonDdtScheme.C lines where the blending with the Euler implicit happens?
thanks


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