Direct numerical simulation, transition mechanisms, compressible boundary-layers, spectral methods, compact finite-difference methods, subharmonic transition, fundamental transition

A method for the direct numerical simulation of transition and turbulence in compressible boundary layers is presented. For the spatial discretization a spectral/finite difference scheme is used. The integration in time is done with a third order explicit Runge-Kutta method. The method is explained in detail, its numerical stability is investigated, and the code is validated by a comparison with results of linear stability theory. Numerical simulations of transition in a flat-plate boundary-layer at a Mach number of 4.5 are presented.