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

TL;DR

This paper introduces a high-order immersed boundary method combining DG techniques and reinforcement learning-based p-adaptation to improve accuracy and efficiency in fluid-structure interaction simulations involving moving boundaries.

Contribution

It presents a novel high-order immersed boundary method with anisotropic p-adaptation driven by reinforcement learning for enhanced FSI simulation accuracy.

Findings

Achieves high-order accuracy in FSI problems

Demonstrates robustness in complex flow scenarios

Enhances near-wall accuracy with adaptive polynomial orders

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.