A physics-infused Immersed Boundary Method using online sequential Data Assimilation

Abstract: A physics-infused 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 penalization method, which are usually selected by the user, are optimized here using an EnKF 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 channel flow with $Re_\tau = 550$. The comparison of the results with a high-fidelity Direct Numerical Simulation (DNS) shows that the data-driven procedure exhibits remarkable accuracy despite the relatively low grid resolution of the ensemble members.