Mixed Lagrangian-Eulerian Data Assimilation for Turbulent Channel Flows

Numerical data assimilation enhances the accuracy of physics-based simulations by integrating experimental measurements, leading to improved forecasts of dynamical systems. In this study, we apply adjoint-based data assimilation to three-dimensional wall-bounded turbulence, focusing on turbulent channel flow at friction Reynolds numbers $Re_{\tau}= 180$. Observations are taken from synthetic particles advected by the flow, with large temporal gaps between measurements addressed through a hybrid Lagrangian–Eulerian approach. Specifically, a Lagrangian solver is combined with an incompressible Navier–Stokes Eulerian solver to reconstruct the velocity field. The key innovation lies in assimilating sparse, non-grid-based data within a subdomain of the computational domain. Despite using observations that are 80 times coarser than the direct numerical simulation (DNS) resolution, the proposed method accurately reconstructs fine-scale flow structures, outperforming standard interpolation techniques. These results demonstrate the potential of physics-informed data assimilation for high-fidelity flow reconstruction from sparse and irregular measurements.