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jdc September 24, 2003 09:27

Crank-nicholson and Pressure correction
Hi all,

I wish to integrate the NS equations using a Crank-Nicholson scheme and a pressure correction algorithm (with dilatable term). I am not confident with the treatment of the term [d(rho)/dt] that appears as a source term of the pressure equation. Has anyone clearly describe the derivation of this term for Crank-Nicholson scheme?

Also: I saw sometimes "Crank-Nicolson" and some other times "Crank-Nicholson". Which one is correct?

Thanks in advance, Julien

Lucas Rainer September 29, 2003 02:08

Re: Crank-nicholson and Pressure correction
"Crank Nicolson" is correct. About the density problem, can you formulate your question more clearly. It is my understanding that d(rho)/dt = (rho_new - rho_old)/delta_t.

For incompressible flow this term is dropped completely. For compressible flow the densities are substituded by the pressure using equation of state - i.e. ideal gas law for example.

qwerty September 29, 2003 06:03

Re: Crank-nicholson and Pressure correction
My be somebody knows was Nicolson man or woman?

Marc October 1, 2003 09:46

Re: Crank-nicholson and Pressure correction
[AFAIK] Crank (male) was Professor at the Brunel University of West-London ( at the Maths Department. Nicolson (female) was one of his PhD candidates. For further information contact somebody working there e.g. Prof. Twizell (who supposed a correction for the C-N scheme needed in some very specific cases)

jdc October 2, 2003 07:17

Re: Crank-nicholson and Pressure correction
I think I have sorted out my problem. Due to the treatment of the momentum coefficient and the decomposition of the pressure, I need to multiply the dilatable term by 1/0.5.

Tnanks for your help and all the precisions on Pr Crank and Dr(?) Nicolson. Julien

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