Input/output analysis of hypersonic boundary layers using hybridizable discontinuous Galerkin methods

We investigate hypersonic boundary layer instability and receptivity for using Input/Output (I/O) analysis. Our approach directly incorporates of effects of multiple modes of instability as well as a model of shock/perturbation interaction to capture receptivity to freestream perturbations. While I/O analysis removes restrictive assumptions underpinning other stability analyses, it requires the solution of large (but sparse) linear systems, and the computational expense remains a pacing challenge. To address this issue, we develop I/O analysis based upon hybridizable discontinuous Galerkin (HDG) methods. HDG provides high-order accuracy and optimal static condensation on unstructured meshes that together significantly reduce the number of degrees of freedom required. We also investigate HDG methods applied to non-conforming meshes that often result from adaptive mesh refinement.