A new family of computational tools is explored in the context of generic problems of interest to Army Research and Development missions. The problems are the SOCBT projectile flow and the MICOM model tactical base flow. Both problems, for which experimental data is available for comparison, have also been extensively computed by other groups with other methods, principally the central difference method of Beam and Warning. Here the techniques we employ and to some extent refine are composite and overset patched mesh systems generated with a new multistep, graphics interactive algebraic procedure FASTWO and the CSCMS symmetric Gauss-Seidel relaxation procedure. The grid generation technique permits comparatively simple direct user control of mesh spacing and quality. The CSCM-S algorithm is an alternating direction space marching method of lines in 2-D and planes in 3-D. The method is economical both in storage and data handling and, also, is rapidly convergent as the result of improved propagation of nonlinear advection, boundary to boundary. In the SOCBT problem the method exhibited convergence in order 100 global iterations and showed improved accuracy vis a vis central difference methods in capturing features of the flow such as shocks and expansions. The method is stable in both elliptic regions and zones of streamwise separated flow including base flow. In the MICOM base flow problem effects of mesh topology and resolution were elucidated.