I know that incompressible and compressible flow solvers are specifically designed to solve different types of problems with different fluid properties/flow conditions. Clearly, among the advantages of using incompressible flow solvers for modeling problems with incompressible fluids is that the energy equation can be neglected, thus reducing the number of variables and equations that need to be solved.
However, I'm curious to know about the accuracy of compressible flow solvers in the limit as the fluid properties and flow conditions tend toward being incompressible. Do compressible flow solvers tend to fail as the fluid/flow being modeled becomes more and more incompressible? Or do compressible flow solvers perform equally well independently of the compressibility of the fluid/flow?
I realize that this question is a bit broad and may very well depend upon the characteristics of the problem being modeled. If such is the case, please help me to understand what factors I need to keep in mind when determining the applicability of using a compressible flow solver where otherwise an incompressible flow solver would suffice.