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 term s are likely to be small. We show that a number of well known approxim ations to the Navier-Stokes equations are valid. Euler equations, para bolized Navier-Stokes equations, potential approximations, Stokes equa tions, all can be used in appropriate regions of the domain occupied b y the fluid. But, unlike in the classical approach, the regions are no t known beforehand but determined by the new model itself as in free b oundary problems. The method is a straightforward adaptation of the X- method introduced by Brezzi, Canuto and Russo but we demonstrate its p ower here and show some new numerical results.