what is the consequence of using compssible method to simulate incompressible flow, like flow in pipe.

It is possible to achieve the generally accepatable results?

thanks a lot

> It is possible to achieve the generally accepatable results?

It depends on the details of the particular compressible scheme.

No compressible scheme will be as efficient as a properly sorted incompressible scheme but there are a small number that are designed to work at low Mach numbers. Of these, most distort and dissipate the acoustics waves by design since this is what causes problems for compressible flow with only a small number attempting to simulate accurate acoustic waves at a non-negligible computational cost.

At zero Mach number (i.e. purely incompressible flow) the compressible flow equations do not really hold although it is not particularly difficult to arrange things so that a compressible code becomes an incompressible code in the limit.

at first there is not any fully-incompressible media in universe, because sound speed is not infinite in any media but incompressible modelling is an assumption.

generally any incompressible assumed flow is a compreesible flow in fact, but with larger sound speed, so theoritically you can use any compressible code for simulation of such flow but computational efficiency may be a serious issue.

Why the computation efficiency is a problem? Should we use much more grid or much smaller time step?

usually time step limitation is issue

The issue with using a compressible code to solve an incompressible (or very low Mach number) problem is very slow convergence. The problem is that the equations become very "stiff" in the sense that the magnitude of the eigenvalues becomes very far apart. The maximum timestep is typically limited by the fastest moving wave. Since the pressure wave moves with the sound speed and the sound speed is very high, the timestep needs to be very low. A preconditioner can be used to bring the eigenvalues closer together for low Mach numbers, thus improving the convergence and the accuracy. But I believe there is a limit to how well they work at very low Mach numbers (<0.01)

thanks a lot. He

dealing with unsteady flow, using compressible code can be computationally tractable, althouth time step is limited but we can use explicite time stepping and so have a fully explicite solver, it is very interesting dealing with large scale problems when solution of system of eq. is difficult, parallel efficiency and scalability of fully explicit methods is surly better than implicit ones.

with looking in literature there several (all speed) compressible solvers that are presented for solution of incompressible flow (artificial compressibility approach)

The artificial compressibility approach is valid only for incompressible flows. I'm not sure I understand what you mean in your last sentence.