Difference between Compressible CFD solver and Incompressible CFD solver
I am a student of CFD.I found one thing really confusing about CFD. Compressible CFD solvers are said to be different from incompressible CFD solver.Most books and lectures cover incompressible flow CFD part.I want to know the fundamental difference between Compressible and Incompressible CFd solver.
Is it possible to develope a flow solver which can be applied for solving both incompressible and compresible? 
In compressible flow solver if I use Favre avarageing ,Jameson algorithm (an explicit method with artificial diffusion for shock capturing)and FVM. Why can it not be used for solving flow for which Mach Number is below 0.3.?

The compressible effects must be considered when the density field varies widely. A incompressible solver cannot be used to solve any compressible problems. In contrast to this, a compressible must give the same solution as incompressible one when compressibility can be neglected.

you mean to say in a compressible flow solver if mach number ranges from 0 to 0.3 it should reproduce the incompressible flow solver results but is there any problem if we use an explicit compressible flow solver with Jameson Algorithm for shock capturing for incompressible flow prediction keeping Mach number below 0.3?

There aren't any shockwaves formed in the flow with Mach in the range as you said. Jameson shock capturing method work well on the shocks, but it is no problem to use the method in the flow without shocks.
In subsonic flow there are only sonic waves, not shock waves. 
The first issue is the mathematical form of the governing equation for compressible and incompressible flows, not the focus on the solver ...
This is the key you have first to study ... then you will be more confident with CFD solver... 
One of the reason of the distinction between compressible and incompressible solvers relates to numerical methods:
 compressible solvers have eigenvalues equal to: uc, u and u+c where u is the velocity and c the speed of sound;  incompressible solvers typically have eigenvalues equal to u. At low mach number, there is a large disparity between the eigenvalues for compressible solver (meaning, the solver has to work harder), but with little to no benefits. In short: a compressible solver can be used to solve incompressible flows but it will take longer than an incompressible one. Julien 
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