I am solving a problem which needs a vast time range computation ranging from micro-second to sub-second. Through computation, the compressible flow(Ma > 0.2) become changed to the incompressible flow(Ma = 0.0~0.2). Due to such change, stability problems can be arisen. That is, under a fixed CFL condition, the compressible solver performs well in compressible flow but it does not work in incompresible flow resulting in collapse of computation.

In the literature, an all speed flow solver which can simulate both compressible and incompressible problems was proposed. The method corrects the value computed by usual compressible methods by an implicit incompressible preconditioner. It is similar to the artificial compressibility method.

Is there anyone knowing the technique to solve mixed-phase(compressible & incompressible)problems?

Thanks in advance.

Are you looking for time accurate results. Usually the preconditioning methods are not time accurate and also another important issue is if you use preconditioning you need to look for the preconditioner that fits your model. There was a review paper by turkel in annual review of fluid mechanics on this. You might want to look up in the references provided in there.

I guess that the preconditioning methods are not only available option. Is there any other good way to treat incompressible flows by compressible solver?

I am finally intending to construct a unified fluid solver regradless of flow phase either compressible or incompressible.

There have been many ways which are proposed for making incompressible code work for compressible flows. The implementation again depends on the kind of incompressible solver you used (SIMPLE, PISO Etc.).

I am mainly using a compressible solver since I am more interested in early phase(mainly compressible). In some applications, I needed to run the compressible code to incompressible states.

My intention is to extend the compressible solver to incompressible flows.

Well, it is easier to extend "incompressible" methods to compressible flows, because they are more general in nature. Nothing prevents you from using a variable density in usual SIMPLE procedure. You may not get a great resolution for all shocks, but looking at your Mach numbers it is not an issue.

Use a transient solver & the following time step, if you want to track the momentum waves (for 2d):

dt = (1/2)*dx/uin

Makes sure your element dimensions are small-enough to track the waves. Use no stabilisation tricks eg. upwinding & it's allies.

Incompressibility assumptions should be good up until M ~ 0.3

Take a look at some of the papers & presentations in <http://adthermtech.com/wordpress3/?page_id=5>

The secret is to observe the simulation during temporal evolution & keep on reducing element size until the waves evolve & track smoothly across the mesh. Try to maintain a fairly uniform mesh without undue distortions. The time step is crucial to your success.

Feel free to e-mail me on <des@adthermtech.com>

mw...

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