SPATIAL DIRECT NUMERICAL-SIMULATION OF HIGH-SPEED BOUNDARY-LAYER FLOWS .1. ALGORITHMIC CONSIDERATIONS AND VALIDATION

A highly accurate algorithm for the direct numerical simulation (DNS) of spatially evolving high-speed boundary-layer flows is described in detail and is carefully validated. To represent the evolution of insta bility waves faithfully, the fully explicit scheme relies on nondissip ative high-order compact-difference and spectral collocation methods. Several physical, mathematical, and practical issues relevant to the s imulation of high-speed transitional flows are discussed. In particula r, careful attention is paid to the implementation of inflow, outflow, and far-field boundary conditions. Four validation cases are presente d, in which comparisons are made between DNS results and results obtai ned from either compressible linear stability theory or from the parab olized stability equation (PSE) method, the latter of which is valid f or nonparallel flows and moderately nonlinear disturbance amplitudes. The first three test cases consider the propagation of two-dimensional second-mode disturbances in Mach 4.5 flat-plate boundary-layer flows. The final test case considers the evolution of a pair of oblique. sec ond-mode disturbances in a Mach 6.8 flow along a sharp cone. The agree ment between the fundamentally different PSE and DNS approaches is rem arkable for the test cases presented.