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-   -   CrankNicolson discretization and Courant number (https://www.cfd-online.com/Forums/openfoam-solving/148275-cranknicolson-discretization-courant-number.html)

Svensen February 8, 2015 07:08
CrankNicolson discretization and Courant number
 
in book it's written that CrankNicolson method is unconditionally stable.

But using this method in icoFoam solver my solution after ~100 iterations explodes... Courant number is >60 at start and increasing (because I have an increasing transient inlet velocity). Yes, Courant number is big, but as I said before CrankNicolson method is unconditionally stable..

So what a problem with simulation ?? Maybe someone got such problem before.

alexeym February 8, 2015 09:00
Hi,

For what type of equations it is unconditionally stable (see the book)?

Svensen February 8, 2015 09:29
According to "Introduction to Computational Fluid Dynamics" 2nd edition" it is written "...schemes with – 1 2 ≤ θ ≤ 1, including the Crank–Nicolson scheme, are unconditionally stable for all values of the time step" ...

calf.Z November 15, 2019 08:30
Quote:
Originally Posted by Svensen (Post 530930)
According to "Introduction to Computational Fluid Dynamics" 2nd edition" it is written "...schemes with – 1 2 ≤ θ ≤ 1, including the Crank–Nicolson scheme, are unconditionally stable for all values of the time step" ...
I am still confused about the instability of CrankNicolson 0.9. Any suggestion?


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