Matrix methods for input-output analysis of 2d and 3d hypersonic flows

Input-output analysis has recently been used successfully to predict the non-modal behavior of small, linear disturbances that can cause laminar to turbulent transition in hypersonic boundary layers. Because input-output analysis does not invoke simplifying assumptions about the spatial growth of the boundary layer, it seamlessly captures the effects of non-modal growth which the linear and parabolized stability theory do not, in particular, it captures the effects of spatial transient growth. Because global analysis requires the solution to large, sparse linear systems which are non-normal and poorly conditioned, a survey of Kyrlov subspace methods is performed, and the usefulness of the GMRES and TFQMR algorithms are also investigated in more detail. For application to 3D flows, a segmented mesh method is then proposed for input-output analysis, and preliminary input-output results are shown for a cone with a highly swept fin at Mach 6.