This work is about the development of a general algorithm for the numerical solution of flow equations: the Navier-Stokes set. This set of differential equations models the time dependent behavior of fluids. It is formed by continuity, linear momentum and an energy transport equations. The algorithm here described is a general one since it can handle equally a great variety of problems, ranging from incompressible to compressible flows, viscous to inviscid, stationary and transient, all of them phisically modeled by the same set of differential equations.

In the present work, a quest for a general algorithm is described, following one of many possible ways to tackle the problem. In general, this is done extending methods either from compressible to incompressible flows or from incompressible to compressible ones.