Direct numerical simulations of laminar viscous layers for supersonic flows are used to study the evolution of naturally occurring as well as externally imposed disturbances under supersonic flow conditions. Receptivity analysis of such flows reveals that artificially produced disturbances (such as wall suction and blowing) have a broad spectrum of wavelength and spectral characteristics. The predictions from linear stability theory reveal that instabilities within the compressible boundary layer are associated with small amplitude disturbances. These in turn, tend to excite the normal modes of the boundary layer, described as T-S type disturbances [1]. The compressibility effects contrast with incompressible studies in the sense that former is associated with (slow/fast) acoustic as well as entropic modes, that arise out of viscous interaction [2].

Such problems find applications in design and testing of supersonic/hypersonic aircrafts, where the fluid structure interaction and flow properties heavily depend on understanding of transition phenomena. Transition; resulting to turbulence has an impact on drag, skin-friction and consequently performance. The receptivity and fluctuation growth/decay are highly sensitive to Mach number, Reynolds number, flow geometry and boundary conditions.

At this stage, it is important to consider some numerical methods developed for linear stability analysis. The system of equations is stiff, with terms of different orders, the compound matrix method (CMM) developed by Somvanshi et. al. [3] has been considered. The approach is to create auxiliary variables from the primitive, and use them to create a new set of compound equations for propagation. The neutral curve for M = 4 is generated using [3]