Stochastic Input-Output Analysis of High Speed Flows

We evaluate the steady-state statistical moments of high-speed flow responses subjected to external stochastic disturbances. To enable these computations at scale, we introduce a streaming framework that mitigates the computational and memory limitations of existing approaches, whose performance typically degrades sharply with increasing dynamical system dimension. Our approach integrates a time‐domain formulation with randomized linear‐algebra–based streaming algorithms that circumvent the explicit formation of high‐order moment tensors, yielding substantial reductions in both computational complexity and memory footprint. The proposed technique enables statistical characterization of complex flow configurations that would otherwise be inaccessible. To demonstrate the utility of framework we compute response second moments in response small amplitude external disturbances. We first validate our approach on a canonical channel flow, demonstrating its accuracy and efficiency in this well characterized setup. We then apply this framework to compressible high-speed boundary layer flows. Our approach remains computationally tractable even for problems with millions of degrees of freedom, enabling new insights into flow sensitivity and transition mechanisms in hypersonic aerodynamic configurations of practical importance.