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CrankNicolson discretization and Courant number

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Old   February 8, 2015, 07:08
Default CrankNicolson discretization and Courant number
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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.
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Old   February 8, 2015, 09:00
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Hi,

For what type of equations it is unconditionally stable (see the book)?
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Old   February 8, 2015, 09:29
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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" ...
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Old   November 15, 2019, 08:30
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Quote:
Originally Posted by Svensen View Post
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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