An immersed boundary method using online sequential data assimilation

A data-driven strategy relying on the Ensemble Kalman Filter (EnKF) is here used to augment the accuracy of a continuous Immersed Boundary Method (IBM). The latter is a classical penalty method accounting for the presence of the immersed body via a volume source term, which is included in the Navier–Stokes equations. The model coefficients of the penalisation method, which are usually selected by the user, are optimised using the data-driven strategy. The parametric inference is governed by the physical knowledge of local and global features of the flow, such as the no-slip condition and the shear stress at the wall. The C++ library CONES (Coupling OpenFOAM with Numerical EnvironmentS) developed by the team is used to perform an online investigation, coupling on-the-fly data from synthetic sensors with results from an ensemble of coarse-grained numerical simulations. The analysis is performed for a classical test case, namely the turbulent plane channel flow with R e τ = 550 . The results, which are compared with high-fidelity Direct Numerical Simulation (DNS), show that the data-driven procedure exhibits remarkable accuracy despite the ensemble members' relatively low grid resolution. The findings present open perspectives of application in dynamic complex systems, such as digital twins. • A methodology combining EnKF and IBM in an online platform is developed, advancing dynamic systems like digital twins. • The method is tested on turbulent channel flow, reducing discrepancies vs. DNS benchmarks compared to classical IBMs. • Heterogeneous data, such as wall no-slip conditions and shear stress, feed the data-driven algorithm for better modelling. • The sensitivity of the data assimilation procedure to grid variations and the number of synthetic sensors is analysed.