CrankNicolson discretization and Courant number

Svensen · February 8, 2015, 08:08

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, 10:00

Hi,

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

Svensen · February 8, 2015, 10:29

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, 09:30

Quote:

Originally Posted by Svensen

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?

February 8, 2015, 08:08	CrankNicolson discretization and Courant number	#1
Svensen Senior Member Join Date: Jan 2015 Posts: 150 Rep Power: 12	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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February 8, 2015, 10:00		#2
alexeym Senior Member Alexey Matveichev Join Date: Aug 2011 Location: Nancy, France Posts: 1,938 Rep Power: 40	Hi, For what type of equations it is unconditionally stable (see the book)?

February 8, 2015, 10:29		#3
Svensen Senior Member Join Date: Jan 2015 Posts: 150 Rep Power: 12	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" ...