Finite element methods of analysis for high speed viscous flows

Over the past three years a finite element based procedure for the solution of high speed viscous compressible flows was developed. The approach followed was to compute steady state solutions via a false transient, using an explicit time stepping scheme, and to attempt to improve the solution quality by incorporating adaptive mesh procedures. The main thrust of the work was to continue on the extension of the approach to the solution of some realistic compressible viscous flows. When flows at high Reynolds number are investigated, is soon becomes apparent that explicit techniwues have to be supplemented if they are to deal effectively with the large variations in element size and aspect ratio which characterize the computational grids necessary for adequate resolutin of the primary flow features. For this reason, the Taylor-Galerkin solution algorithm was rewritten in an explicit/implicit form. Solutions were computed for the problems of a flow past a flat plate, M-3, Re-100; shock/boundary layer interaction, M-2, Re-296000; flow over a compression corner, M-11.68, Re246000; and unifrom flow past a circular cylinder, M-6.34, Re-39770. A summary of the results is included and demonstrates the numerical performance of the scheme.