A High-Order Immersed Boundary Method for Fluid-Structure Interaction Problems

TL;DR

The paper addresses the challenge of accurate and efficient fluid-structure interaction with moving immersed boundaries. It introduces a high-order discontinuous Galerkin immersed boundary method (DG-IBM) that uses volume penalization and is coupled in a partitioned fashion to rigid and elastic structures. A reinforcement-learning–driven anisotropic $p$-adaptation strategy concentrates resolution near the moving interface and in vortical regions, yielding higher accuracy at a smaller cost. Validation on a pitching airfoil, stall flutter, and flow-induced vibration behind a cylinder demonstrates robust high-order accuracy and notable efficiency gains from adaptive resolution.

Abstract

Accurate and efficient simulation of fluid-structure interaction (FSI) problems remains a central challenge in computational physics. High-order discontinuous Galerkin (DG) methods offer low numerical errors and excellent scalability on modern architectures, making them attractive for high-fidelity FSI simulations. This study presents a high-order immersed boundary method (IBM) for FSI problems which combines a volume-penalization approach with a high-order nodal DG solver. To improve near wall accuracy, an anisotropic p-adaptation strategy based on reinforcement learning is used to dynamically adjust the polynomial orders in the mesh elements located near the moving immersed boundaries. By doing so, we show enhanced accuracy with a limited increase in computational cost. Accurate evaluation of surface forces is achieved using symmetric high-order Gaussian quadrature on immersed boundaries. The proposed method is coupled with both rigid-body and elastic-structure solvers within a partitioned framework. Numerical validations using a pitching airfoil, stall flutter of an airfoil, and flow-induced vibration of an elastic beam behind a cylinder demonstrate high-order accuracy and robustness. These results indicate that the present approach provides an effective and scalable strategy for complex moving-boundary FSI simulations.

Figures (14)

• Figure 1: Time histories of (a) $C_L$, (b) $C_D$, and (c) $C_M$ for the pitching airfoil compared with the reference data of Xia et al.xia2024stall.
• Figure 2: Snapshots of the flow around a pitching airfoil with $p=3$: (a) IBM mesh and moving immersed boundary; (b) vorticity field showing unsteady vortex evolution.
• Figure 3: Convergence and accuracy comparison for the pitching airfoil cases: (a) Relative error $E$ of $C_L$, $C_D$, and $C_M$ versus $1/h$ with uniform $p=3$; (b-d) force coefficient errors for the $p$-adaptation case compared with the uniform $p=3$ results.
• Figure 4: Snapshots of the flow around a pitching airfoil with $p$-adaptation: (a) distribution of the average polynomial order in each element; (b) vorticity contours.
• Figure 5: Time histories of (a) angle of attack $\alpha$, (b) angular velocity $\omega$ for the airfoil stall flutter compared with the reference data of Xia et al.xia2024stall.