Hi Everton,
Mathematica is an excellent tool, but like any tool it has limitations. This type of problem -- a system of nonlinear partial differential equations -- is usually approached with very highly developed, and very expensive, finite element analysis software. An example is Comsol Mulitphysics, but there are many more. And even for these tools, fluid dynamics is a difficult problem. In the laminar flow regime, solutions are usually not difficult. As the Reynolds number increases, approaching turbulence, the stability of the numerical solution becomes an issue. In the turbulent regime, there is no steady state solution for the flow, and a direct time dependent solution is needed. However, the turbulent eddies become very detailed, and the mesh needed can become so fine that not even a supercomputer can handle the problem.
So, in short, if I could have only one tool it would be Mathematica, because of its versatility. But there is still a need for specialized tools which are not as broad, but much deeper in their particular subject. I think this is one such case, and it is not realistic to expect Wolfram to provide the capability in Mathematica. (I would welcome being proven wrong!)
Kind regards,
David
