I have been told recently that assuming incompressible flow does not simplify CFD simulation and does in fact increase numerical dificulties and complexity greatly. Is this true and if so why? What does the incompressible assumtion do numerically to cause problems (this is all at v low mach numbers by the way, i.e. no where near supersonic). Anybody got any references that might be of use.

Iterative method doesn't converge well might be one aspect. Some zero diagonal entries in Jacobian matrix induced from incompressible equation.

I have worked on numerical methods for both incompressible (viscous) and compressible (inviscid) flow and I am not sure that one is necessarily simpler than the other. Both regimes definitely have their own share of challenges.

In incompressible flow, the pressure propagates at an infinite speed and hence a disturbance is instantly "felt" everywhere in the flow. Furthermore, in the incompressible Navier-Stokes equation, there is no explicit equation to use to solve the pressure. The pressure is obtained by coupling the momentum equations with continuity, usually through iterative methods like the SIMPLE family of methods. In contrast, when solving compressible inviscid flow, pressure is obtained through an equation of state.

Actually by combining the momentum and continuity equations, an explicit equation can be obtained for the pressure -- the Poisson pressure equation. Although this provides an explicit equation for the pressure, some numerical method that use this formulation may experience difficulty keeping the flow everywhere divergence free.

Two good references are Tannehill, Andersen, and Pletcher's Computational Fluid Mechanics and Heat Transfer and Patankar's Numerical Heat Transfrer and Fluid Flow.

Ryoga