In joint work with T. Chan (University of California, Los Angeles) and W-P Tang (University of Waterloo), preconditioning methods for nonself-adjoint advective-diffusive systems based on a non-overlapping Schur complement domain decomposition procedure for arbitrary triangulated domains will be discussed. In our implementation of the Schur complement preconditioning technique, the triangulation is first partitioned into a number of non-overlapping subdomains. This partitioning induces a natural 2x2 partitioning of the p.d.e. discretization matrix. By considering various approximations to the 2x2 system inverse, we consider a family of robust preconditioning techniques suitable for parallel computing architectures. A computer code based on these ideas has been coupled to an approximate Newton solver for the discretized Euler and Navier-Stokes equations governing compressible fluid flow. Our implementation, utilizing MPI message passing protocol, has been tested on the IBM SP2 and the SGI Power Challenge array. More recently, we have considered implementations suitable for scalable shared memory parallel computing architectures such as the SGI Origin2000. Performance characteristics of these codes will be shown for a variety of realistic subsonic and transonic fluid flows occurring in aerodynamic performance analysis.