SIMPLE algorithm for compressible flow
dear all, I understand we need SIMPLE algorithm for incompressible flow because there is no equation for pressure. but why do we use it for compressible flow although we can get pressure field by means of ideal gas law?
thanks in advance. 
Re: SIMPLE algorithm for compressible flow
The reason many people extend the simple algorithm for compressible flows is for using a single unified solver which is valid over the entire flow regime. Many algorithms which are developed for compressible flows are extended to incompressible flows through preconditioning for the same reason. Also in certain flow scenarios, there may be wide variations of the mach number in the flow region and hence an unified solver is a better way of handling it.

Re: SIMPLE algorithm for compressible flow
very clarifing answer !. thanks a lot sir

Re: SIMPLE algorithm for compressible flow
Dear Harish. The answer is very clear and I love it. Can I ask you something on the difference bewteen two approaches for all speed flows(i.e., varies from compressible to imcompressible): the compressible flow scheme with a preconditioning and the incompressible flow scheme such as SIMPLE. Which one is better from all speed flows in terms of accuracy, solution quality, stability and efficiency. Which one is better to begin from scratch? On the other hand, which one is a generall unified approach for such flows? Thanks in advance and once again for clear classcification.

Re: SIMPLE algorithm for compressible flow
I do not have any experience developing pressure based solvers using algorithms such as SIMPLE or PISO. From what i heard, there are certain mach number restrictions on the application of the pressure based algorithms at high mach numbers. As for the preconditioning technique, there is a problem with interpreting the exact time in your computations and if your results need to be tine accurate there might be some problems with using preconditioning with the compressible solvers. Regarding accuracy, solution, stability etc. it depends more on the discretization schemes that you employ for making the computations rather than the fact its pressure based or density based.

Re: SIMPLE algorithm for compressible flow
The main difference is the approach for density variation.
The SIMPLe type algorithm seek for pressure correction with some assumption or simplification. (look into peric's book for more detail). In other words, we first have an approaximate velocity field, for this we wish to correct it such that continuity satisfies. The velocity correction are expressed in terms of pressure correction and thus we get pressure correction equation, that is solved to get new pressure field. When the flow is compressible, the SIMPLE type method goes little further and relate density change to pressure correction. Since flux is related to density change, this could also be included into pressure correction equation. This way you get pressure correction and you update velocity and density. Density based solvers work on flux balances directly i suppose. 
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