A high-order discontinuous Galerkin framework combining volume-penalization immersed boundaries and dynamic p-adaptation for moving-body and fluid-structure interaction simulations

Abstract

This study presents a high-order numerical framework for fluid-structure interaction (FSI) problems involving rigid motion or deformable elastic solids subjected to low Reynolds number viscous flow. The Navier-Stokes equations in the fluid domain are solved using a high-order nodal discontinuous Galerkin (DG) solver HORSES3D, which is combined with a volume-penalization immersed boundary method (IBM) for moving boundaries. The dynamic p-adaptation strategy based on reinforcement learning is used to adjust the polynomial orders near the moving immersed boundaries, which improved accuracy with a limited increase in computational cost. The aerodynamic forces on FSI interface are evaluated using symmetric high-order Gaussian quadrature accurately. The fluid solver is coupled with both rigid-body and elastic-structure solvers using a partitioned coupling strategy. The framework is validated through three numerical test cases, including pitching airfoils, stall flutter of an airfoil, and the flow-induced vibration of an elastic beam behind a cylinder. The results demonstrate the robustness of the proposed framework and its ability to achieve at least second-order accuracy in FSI simulations, showing the applicability of the framework for the considered FSI or moving-body flow problems.