Hybridizable Discontinuous Galerkin methods for Input/Output Analysis of Complex Hypersonic Boundary Layers

The increasing complexity of hypersonic flight simulations necessitates advanced numerical methods that can reduce computational time while maintaining accuracy. This is especially important for calculations predicting the transition of hypersonic boundary layers from laminar to turbulent flow, in which complex geometry and multi-modal effects play a significant roles. This research explores the efficacy of Hybridizable Discontinuous Galerkin (HDG) methods combined with Adaptive Mesh Refinement (AMR) to support Input/Output (I/O) analysis to understand the stability and receptivity of complex hypersonic boundary layers. Specifically, we apply these methods to analyze the behavior of acoustic waves in hypersonic conditions. Our approach leverages the common requirement of a linear system from HDG and I/O analysis to study the response of the flow field to small perturbations around a steady baseflow, allowing for detailed examination of wave propagation and stability characteristics. The results demonstrate the HDG-AMR method, along with I/O analysis, as a tool for hypersonic flow problems as it accurately resolves wave dynamics and flow features in hypersonic boundary layers. This research sets the foundation for future refinement and optimization of the method.