Numerical Solution of Parabolized Stability Equations Using Super-Compact Scheme

The super-compact finite difference method is used to develop a highly accurate finite difference PSE code to investigate the stability analysis of incompressible boundary layers over a flat plate. The PSE equations are derived in terms of primitive variables and are solved numerically using super compact method. In these formulations, both nonparallel as well as nonlinear effects are accounted for. The validity of the present numerical scheme is demonstrated using spatial simulations of two cases; two-dimensional (linear and nonlinear) Tollmien-Schlichting wave propagation and three-dimensional subharmonic instability breakdown. The PSE solutions have been compared with previous numerical investigations and experimental results and show good agreement.