Three-dimensional flow analysis and applications with parallel finite element methods

This thesis presents High Performance Computing (HPC) tools for flow simulations involving large-scale 3D computations on parallel platforms. Finite element formulations for the Navier Stokes equations are used in the simulations. These formulations contain the streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) stabilizers (for incompressible flows), or a combination in the form of Galerkin/Least-squares stabilizers. These stabilizations circumvent potential numerical oscillations due to advection terms, and due to the use of equal order interpolations for velocity and pressure in the incompressible case. The implementations include a data-parallel style on a Thinking Machine CM-5, a message-passing paradigm on a CRAY T3D, and a shared-memory model on a multiprocessor SGI ONYX. All implementations are based on implicit strategies with no assumptions on the structure of the mesh. The GMRES iterative update technique is used for the solution of the nonlinear equation systems arising from the discretizations. For very large-scale computations matrix-free techniques are utilized to reduce memory requirements. A method which uses sparse matrix operations within the matrix-vector products in GMRES is developed on the CRAY T3D. The sparse storage scheme enables testing of more sophisticated preconditioning techniques other than diagonal scaling. Base flows around circular cylinders and spheres are simulated to establish confidence in the accuracy of the implementations. Subsequently, aerospace applications arising in modern transportation are simulated. These involve the dynamics of ram-air parachutes and compressible flow around high-speed trains crossing in a tunnel. The parachute simulations include inflation, steady-glide and the flare maneuver.