Unsteady flow enhancement on an airfoil using sliding window weak-constraint four-dimensional variational data assimilation

This study establishes a continuous sliding window weak-constraint four-dimensional variational approach for reproducing complete instantaneous flow from sparse spatiotemporal velocity observations. The initial condition, boundary and model-form uncertainties are corrected simultaneously by spatiotemporally varying additive forcing, coupled with the large eddy simulation (LES) framework, which reinforces subgrid-scale viscosity stresses simplifies gradient computation. force undergoes Stokes–Helmholtz decomposition to ensure divergence-free projection natural pressure determination. model is theoretically derived minimize discrepancies between observations numerical predictions of primary-adjoint system, enabling optimal contribution force. Synthetic data fine-grid LES vortical over an NACA0012 airfoil used as algorithm evaluated on benchmark case, where subsampled at 1/400 000 resolution required LES. strategy expands dependence domain mitigates impact chaos, achieving 90% pointwise correlation filtered parameters 80% spectral all resolved wavenumbers. Despite lack near-wall observations, streaks accurately recovered due convective sensitivity outer flow. While fluctuation in inflow region not well excited LES, recovery augmented downstream. In both inner wall layers, distributions obtained reasonably capturing signatures structure their downstream convection. robustness observation noise demonstrated. Finally, temporal estimation evaluated, establishing threshold successful reconstruction.