Hellow,

Basically, SIMPLE is a pressure-correction method for imcompressible flow. But in some commerical CFD software, SIMPLE is also used to analyze the compressible flowfield.

It is very common for me to deal with the transonic and supersonic compressible flowfields. I don't konw if SIMPLE will cause some problem for predicting the comressible flowfield and if it will omit some detailed flowfield phenomenon (for example, shock and boundary layer).

Thanks!

Jing

Jing

(1). The best way to do is to try it out, I mean run some cases using commercial codes with transonic or supersonic conditions. (2). As an example, Fluent/UNS is pressure-based incompressible formulation, while Fluent/Rampant is density-based compressible formulation. (3). So, it is well-recognized that there is limit to the pressure-based formulation when used for transonic, supersonic flows. (4). But there are always tricks one can invent, so you will have to address it on the individual bases(codes). In general, it is a good idea (actually it is a rule), to use density-based formulation for transonic and supersonic applications. (It is part of the history in cfd development)

Thanks for your opinion.

Could you tell me what is the limit of pressure -based foumulaltion when used for transonic and supersonic flow and what are the tricks one can use for pressure-based formulation used for transion and supersonic flow?

Thanks!

Jing

In principle, there is no limit to pressure-based method. Several all-speed pressure-based methods are discribed in the past few years. Go to a library, you can find a lot of info. in AIAA J. or in Wei Shyy's book.

The extension of SIMPLE to such flows was done a very long time ago, i.e. in the 70s. I recall papers by Issa, Spalding, and later by McGuirk, Raithby, Parameswaran and others. The shock capturing can be poor sometimes, and a remedy for this was proposed by McGuirk and Page, AIAA J,28, 1990.

You are right. A lot of PISO-extend algorithms have also appeared after McGuirk and Page's paper. Actually, the shock-capturing capability has more to do with the discretization of the convection term, rather than the pressure-velocity coupling.

Yes, I agree that the discretisation scheme for convection is a significant factor for shock capture as most SIMPLE-based codes use Hybrid or pure upwind as the default. A non-linear higher-order scheme produces a much sharper shock.

Although a non-linear higher-order scheme produces and fine grid are important for schock, I think the basic problem is still the SIMPLE method.

I have tried a commerical code with 3 order discritization to calculte a supersonic flowfield in a nozzle, but it still can not get the detailed shock as another dommestic software which is especially for compressible flowfield.And also the boundary layer.

Extensions to SIMPLE for such flows have already been discussed. Commercial codes may differ in their precise treatment, and so I suggest that you ask the vendors for details of how they have extended SIMPLE.

Incidently, I have known shocks to be predicted incorrectly because of inconsistencies in the discretisation of the momentum convection and continuity convection terms. This qualifies as a formulation error rather than a software bug, which is another possibility.