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: 11	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.

Thread Tools	Search this Thread
Show Printable Version Email this Page	Search this Thread: Advanced Search
Display Modes
Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Running stably with a large Courant number using pimpleFoam	mlawson	OpenFOAM	11	November 29, 2014 11:37
should Courant number always be kept below 1?	wc34071209	OpenFOAM Running, Solving & CFD	16	March 9, 2014 20:31
OpenFOAM, Courant number and implicit methods	fsaltara	OpenFOAM	8	December 28, 2012 05:16
ddt explicit or implicit with courant number!!	mrshb4	OpenFOAM	0	December 13, 2010 12:13
Courant number	msrinath80	OpenFOAM Running, Solving & CFD	1	May 29, 2006 18:20

February 8, 2015, 10:00		#2
alexeym Senior Member Alexey Matveichev Join Date: Aug 2011 Location: Nancy, France Posts: 1,938 Rep Power: 39	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: 11	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" ...