Physics-informed neural networks modeling for systems with moving immersed boundaries: application to an unsteady flow past a plunging foil

TL;DR

This work addresses unsteady flows past moving immersed boundaries by introducing two immersed boundary aware PINN variants: MB-PINN, which solves the fluid NS equations in a fixed Eulerian grid, and MB-IBM-PINN, which augments the physics loss with solid-region terms. They demonstrate pressure recovery and velocity reconstruction for a plunging, 2D elliptic foil at $Re=500$, using a fixed-domain IBM description and comparing recovered pressure against an ALE solver. A fluid–solid partition of the physics loss, with weights $\lambda_{fluid}$ and $\lambda_{solid}$, reveals that MB-PINN can outperform MB-IBM-PINN when solid motion is known a priori, while MB-IBM-PINN can match MB-PINN under suitable weighting; data-efficiency is further enhanced via a physics-based vorticity-cutoff sampling strategy, achieving large data reductions with preserved accuracy. The findings establish data-efficient, non-body-attached PINN surrogates for complex moving-boundary flows and point to future work on adaptive loss balancing and parametric generalization for broader applicability.

Abstract

Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady flows past moving bodies, such as flapping wings is scarce. Earlier studies mostly relied on transferring to a body attached frame of reference which is restrictive towards handling multiple moving bodies or deforming structures. Hence, in the present work, an immersed boundary aware framework has been explored for developing surrogate models for unsteady flows past moving bodies. Specifically, simultaneous pressure recovery and velocity reconstruction from Immersed boundary method (IBM) simulation data has been investigated. While, efficacy of velocity reconstruction has been tested against the fine resolution IBM data, as a step further, the pressure recovered was compared with that of an arbitrary Lagrange Eulerian (ALE) based solver. Under this framework, two PINN variants, (i) a moving-boundary-enabled standard Navier-Stokes based PINN (MB-PINN), and, (ii) a moving-boundary-enabled IBM based PINN (MB-IBM-PINN) have been formulated. A fluid-solid partitioning of the physics losses in MB-IBM-PINN has been allowed, in order to investigate the effects of solid body points while training. This enables MB-IBM-PINN to match with the performance of MB-PINN under certain loss weighting conditions. MB-PINN is found to be superior to MB-IBM-PINN when {\it a priori} knowledge of the solid body position and velocity are available. To improve the data efficiency of MB-PINN, a physics based data sampling technique has also been investigated. It is observed that a suitable combination of physics constraint relaxation and physics based sampling can achieve a model performance comparable to the case of using all the data points, under a fixed training budget.

Figures (16)

• Figure 1: Schematics of the problem setup: computational domain $\Omega$ is chosen for the IBM solver, and the truncated domain $\Omega^r$ is chosen for the surrogate model. $\Omega_f$ and $\Omega_f^r$ are the fluid regions excluding the solid boundary $\Gamma_{IB}$ and solid region $\Omega_s$ at any given time instant. $\Gamma_{inlet}^r,$$\Gamma_{outlet}^r,$$\Gamma_{upper}^r$ and $\Gamma_{lower}^r$ are the inlet, outlet, upper and lower boundaries of the truncated domain $\Omega_r$, respectively.
• Figure 2: Schematics of (a) a representative computational domain $\Omega = \Omega_f \cup \Omega_s$ used in the immersed boundary method. Here $\Omega_s$ is the shaded area representing the solid region bounded by the solid boundary $\Gamma_{IB},$ and (b) the mesh grid representing the staggered primitive variable arrangement and fluid-solid grid point classifications.
• Figure 3: Schematic of (a) MB-PINN and (b) MB-IBM-PINN network architectures used under the present IBA framework
• Figure 4: A schematic representing sampling of residual, bulk and boundary data points at two different time instants in (a) and (b). Although in the present work, bulk data points and fluid region residual points are sampled from same Eulerian grid, the bulk data points and fluid residual points are shown to be disjoint considering a more general case.
• Figure 5: (a) Spatial grid of CI data set with the Lagrangian markers in blue, inlet and wall boundary points in magenta, and the solid region in red colours, respectively. Zoomed view of the spatial grid for (b) CI, (c) Ref-IBM and (d) Ref-ALE presents the comparative spatial resolution near the solid boundary.