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

"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.

My be somebody knows was Nicolson man or woman?

[AFAIK] Crank (male) was Professor at the Brunel University of West-London (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 C-N scheme needed in some very specific cases)

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