Linear stability analysis of discontinuous boundary layer profiles with shock capturing schemes

Modal linear stability analysis is performed on flat plate hypersonic self-similar, zero pressure gradient boundary layer profiles containing strong discontinuities due to the presence of the leading-edge shock wave. For this investigation, a planar wedge with half-angle of 5 degrees is placed in Mach 8 flow at free-stream unit Reynolds number 1.6E7 1/m. Boundary layer edge conditions, and exact location of the shock wave, then follow from oblique shock relations and permit baseflow computation. To capture flow discontinuities in time-asymptotic analyses, we introduce WENO schemes to the discretized generalized complex non-symmetric linear stability eigenvalue problem. The linearized Navier-Stokes equations are discretized with WENO schemes which split the linear fluxes into positive and negative parts and treat them with appropriate WENO differential operator, shown to depend only on the steady-state solution. It is demonstrated that present WENO implementation significantly reduces the amplitude of spurious oscillations introduced to eigenfunctions near strong discontinuities by standard finite-difference or spectral discretization schemes. Presently, the work is being extended to BiGlobal modal analysis aiming to incorporate shock waves present on blunted geometries.