Data-driven physics-informed and immersed boundary aware surrogate modeling of unsteady flows past moving bodies
Résumé
Unsteady flows past rigid or flexible moving bodies such as flapping wings are characterised by complex non-linear interactions across spatial and temporal scales. These flow field characteristics can be resolved using high-fidelity computational fluid dynamics approaches such as immersed boundary methods (IBM), simulating such unsteady flows on a fixed Eulerian grid. As a result, IBM avoids re-meshing at every time step, saving a lot of computational effort as compared to arbitrary Lagrangian-Eulerian (ALE) formulation. Imposing the fluid-solid interface boundary conditions in IBM framework remains a non-trivial problem for which discrete forcing IBM[1] is one approach used in the present study. Moreover, these simulations are still memory intensive and computationally costly for large parametric sweeps. Hence, there is a need for surrogate modeling frameworks that can capture/ handle the moving bodies effectively, and at the same time, are computationally efficient for real time prediction, queries or allied inverse problems. Recently, physics informed neural networks (PINNs)[2, 3] have emerged as a viable approach for modeling complex forward and inverse problems in fluid mechanics in a data efficient manner. PINNs have been recently tested for flow past a single moving body using conformal/rigid body transformations[4], but they are not practical in the case of multiple moving bodies or flexible structures. Thus, emulating IBM through PINNs would be beneficial. In this direction, Huang et. al [5] developed an immersed boundary based PINN that was used to solve steady state flow past a fixed cylinder. More recently, based on the fictitious domain method (FDM), Yang et. al [6] proposed PINNs to solve linear elliptic and parabolic PDEs involving a fixed and a moving body, respectively. Further extending the work of Huang et. al [5] and Yang et. al [6], we propose an immersed boundary aware PINNs (IBA-PINNs) methodology for surrogate modeling. We use this framework in the case of unsteady incompressible flow past a plunging airfoil against different plunging amplitudes. In addition, we propose a sequential learning strategy coupled with partitioned physics loss weighting to improve the predictions in the fluid domain. Here, the training data for IBA-PINNs has been generated using an in-house discrete forcing IBM[1] based unsteady flow solver.