On simulation and analysis of instability and transition in high-speed boundary-layer flows

The simulation of instabilities and laminar-trubulent transition in high-speed boundary-layer flows represents one of the major computational challenges of the decade. By taking advantage of recent advances in computational science and instability theory for compressible flows, we have formulated an approach to this problem that combines parabolized stability equation (PSE) methodology with spatial direct numerical simulation (DNS). The relatively inexpensive PSE method is used to explore the parameter space, to compute the early (weakly and moderately nonlinear) stages of laminar breakdown, and to provide inflow conditions for the spatial DNS, which is then used to compute the highly nonlinear laminar-breakdown stage. The approach is made feasible by an accurate and efficient DNS algorithm, which has been implemented in parallel on a CRAY C90 supercomputer. The design of the DNS algorithm is discussed in detail, with emphasis on factors that affect both accuracy and efficiency. The method is applied to the investigation of the laminar breakdown of the boundary layer on an axisymmetric sharp cone in Mach 8 flow. Techniques for analysis of the resulting data are also addressed, including novel computational flow imaging procedures.