Cranknicholson and Pressure correction
Hi all,
I wish to integrate the NS equations using a CrankNicholson 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 CrankNicholson scheme? Also: I saw sometimes "CrankNicolson" and some other times "CrankNicholson". Which one is correct? Thanks in advance, Julien 
Re: Cranknicholson 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. 
Re: Cranknicholson and Pressure correction
My be somebody knows was Nicolson man or woman?

Re: Cranknicholson and Pressure correction
[AFAIK] Crank (male) was Professor at the Brunel University of WestLondon (www.brunel.ac.uk) 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 CN scheme needed in some very specific cases)

Re: Cranknicholson 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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