I'll be very grateful for any reference to books or articles about pressure-based NS-solver for variable density flows

Best regards

(1). Pressure-based methods are not limited to the incompressible flows. (2). You can find the description of the method in many CFD books, check the CFD books online section of the Resources at this website. Also check out the previous messages posted here about the CFD books .(3). There is also an article in AIAA Journal Vol.36,No9,Sept 1998, on "Pressure-Based Compressible Calcualtion Method Utilizing Total Variation Diminishing Scheme" by Issa from Imperial College. It has supersonic flow samples with shock waves. If your interest is in supersonic flow, you can look into it. (I did not have the time to read it.)

The following paper would be of help to you because it describes details:

"A Collated Finite Volume Method For Predicting Flows At All Speeds"

I. Demirdzic, Z. Lilek and M. Peric

International Journal for Numerical Methods in Fluids Vol. 16, p.1029-1050, 1993

Hi,

You should aslo check out some of the work by Gerry Schneider of U Waterloo, he and some of his co-workers have developed some interesting all-speed pressure based algorithms in the control volume finite element framework. I do not have the references handy at this time, as I am on holiday. However, I did see him present some related work at the CFD 99 conference in Halifax this year and the it is in the proceedings and the references will get you started! I think that I also glanced at a paper in the International Journal of Numerical Heat Transfer a few months ago.....but I can't say which volume for sure.

The work at the conference was in fact for Bousinesque (sp??) approximation variable density flows and may be of interest to you!

Actually, looking the references up for yourself is a very good exercise. As Niche (spelling???) put it: "What does not kill you makes you stronger"...or something like that!

Good Luck.............Duane

Thank You for all the responses,

my variable density is connected not with the compressibility, but with the stratification, namely, with the water-air interface. Thus compressible methods do not suit due to the lack of the equation of state, if not to use the artificial compressibility.

With best regards

I did not know that there is no equation of state for water. Is it because water is so unusual component, or is it in a liquid state? I hope there is an equation of state for air.

Andrzej Matuszkiewicz

Thank You for the answer,

water is in liquid state, and Mach number is 0. In this case, to search solution as a limit of near zero Macn number could be very difficuilt, because of too greate difference in sound speeds. Also, my question was not so phylosophical, I need just any examples of classical SIMPLE-type methods for non-uniform (better very non-uniform, as for water-air system) density.

With best regards

For a stratified gas-liquid flow have a look at

Int. j. numer. methods fluids Vol. 16, 967-988 (1993)

Andrzej