Numerical Assessments of Data Assimilation Methods for High-Speed Flows

Data assimilation (DA) in high-speed shock dominated flows demands repeated and expensive integrations of the Euler equations, making real time inference and uncertainty quantification impractical. To address this, we develop a reduced-order surrogate for the one dimensional Sod shock tube problem using a convolutional autoencoder whose latent representation is advanced in time by a learned discrete-time mapping network. This surrogate accurately captures the evolution of the shock, contact discontinuity, and rarefaction at a cost of orders of magnitude lower than the full solver. We then embed this autoencoder‐based model within four representative DA frameworks: (a) ensemble Kalman filter (EnKF), (b) four-dimensional variational assimilation (4D Var), (c) adjoint-free forward sensitivity method (FSM) and (d) particle filter (PF) to assimilate sparse, noisy observations on a coarse grid. We compare their performance through root mean square error in density, velocity, and pressure; the fidelity of posterior uncertainty; and overall computational efficiency. Our comparative evaluation reveals which data assimilation method provides the best balance of accuracy, speed, and implementation complexity for compressible shock-dominated flows. By enabling surrogate-assisted assimilation, these findings pave the way for digital twin development, real time flow control, and rapid decision-making in aerospace systems.