Data-driven physics-informed and immersed boundary aware surrogate modeling of unsteady flows past moving bodies

  • Sundar, Rahul (Department of Aerospace Engineering, IIT Madras)
  • Majumdar, Dipanjan (Department of Aerospace Engineering, IIT Madras)
  • Lucor, Didier (Laboratoire Interdisciplinaire des Sciences du Numérique (LISN))
  • Sarkar, Sunetra (Laboratoire Interdisciplinaire des Sciences du Num´erique (LISN))

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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.