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 $R{e}_{\tau }=550$. 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.