A coupled immersed boundary method and isogeometric shell analysis for fluid–structure interaction of flexible and lightweight shells in high-Reynolds number flows

Abstract

This study presents an efficient numerical framework for simulating fluid–structure interactions (FSIs) involving flexible, lightweight shells subjected to high-Reynolds-number flows. By combining the immersed boundary method (IBM) and isogeometric analysis (IGA), the framework incorporates three major innovations: (1) a wall-modeling, direct-forcing, diffused-interface IBM tailored for FSI simulations with high-Reynolds-number turbulent flows, employing non-equilibrium explicit wall functions; (2) integration of the interface quasi-Newton inverse least-squares (IQN-ILS) method into the IBM/IGA framework to enhance the accuracy and efficiency of iterative Gauss–Seidel coupling in strongly coupled FSI scenarios; and (3) high-order solvers for both fluid and structural domains, featuring a sixth-order compact finite difference method (FDM) for fluid dynamics and isogeometric shell formulations for structural analysis. The framework is validated through four numerical test cases, including simulations of a hinged flag, an inverted flag, a membrane airfoil, and an air-supported membrane structure. The results demonstrate good agreement with reference data, showing the framework’s efficiency, accuracy, and applicability for solving large-scale shell-related FSI problems across diverse engineering and scientific domains.