THE CHI-METHOD FOR THE NAVIER-STOKES EQUATIONS

We justify partially a well known methodology of fluid mechanics which consists in simplifying the Navier-Stokes equations when certain terms are likely to be small. We show that a number of well known approximations to the Navier-Stokes equations are valid. Euler equations, parabolized Navier-Stokes equations, potential approximations, Stokes equations, all can be used in appropriate regions of the domain occupied by the fluid. But, unlike in the classical approach, the regions are not known beforehand but determined by the new model itself as in free boundary problems. The method is a straightforward adaptation of the X-method introduced by Brezzi, Canuto and Russo but we demonstrate its power here and show some new numerical results.