Hello gentlemen, i'd like to start a discussion on pressure based methods (SIMPLE, PISO etc) i am familiar with time based approaches (unsteady formulation) as that's what i've learned in my classes. however pressure based approaches seem very popular especially for steady incompressible flow. i'd like if we can provide descriptions of these methods, references, implementation of boundary conditions, application to compressible and unsteady flows, comparision to time based approaches and anything else you might think appropriate. I'd like to do this for the benefit of the forum as well as for my own personal edification. even though these schemes are considered "old" i think they are implemented in many commercial packages so i think i'd be good to discuss them.

(1). You can not survive in the outside world without knowledge of low speed flow CFD. It is not the code, not the method, but the physics. (2). It would be a good idea that you can convince your department to offer such graduate course so that you have a chance to do some home work exercises. A special study under the guidance of a professor is also practical. (3). I am sure that at the place where you study, there should be professors knowledgable enough to offer some help. (4). The relatively light discussions here can not provide you any additional information which you already have access to at the university. (5). I think, it can be a very good post-doctor research subject. (6). Well, anyway, you are always free to ask any specific question here. (7).I think, most of these pressure-based codes were derived from the original work by researchers at the Imperial College. A post-doctor study at Imperial College should be a very good idea to learn the pressured based methods. (it is just an idea. )

Your idea is interesting. However someone should lead the debate! I suggest the following first question : Which known numerical methods fall in the category of pressure correction methods?

I would recommend the book by S.V. Patankar, "Numerical Heat Transfer and Fluid Flow" (Hemisphere Publishing, 1981, I think). It is very clearly written and gives enough information to write your own SIMPLE code.

In general, the idea of SIMPLE is that the momentum equation is solved with a guessed pressure field. If the guess was correct, the resulting velocity distribution will satisfy continuity. If it was incorrect, the pressure is guessed again using the continuity equation as a guide. The solution thus proceeds by repeatedly solving momentum and continuity, until continuity is satisfied. The book will make this clearer. The method is very versatile and can be used for both incompressible and compressible flows. I suppose it is most suited to incompressible, steady flow (elliptic governing equations). Good luck.

Regards,

Peter

This topic is very interesting. I have gone a reversed route as yours: earlier pressure correct method and later time marching method. I have seen a very interesting defference in the calculation of flow in diffusor: With the pressure correct method you'll get a symmetric flow field for a symmetric geometry, whereas you'll get a non-symmetric flow separation for a symmetric geometry with the time marching method. The later agrees well with reality. Maybe the pressure correct method stablizes the flow strongly and hence is not suitable for many flows.

X. Ye