Moving mesh fluid–structure interaction approach for vortex-induced vibration simulation based on the discontinuous Galerkin method with adaptive mesh refinement technique

Vortex-induced vibration (VIV) remains a fundamental yet computationally challenging problem in computational fluid dynamics. This study develops a moving mesh fluid–structure interaction approach within a Runge–Kutta discontinuous Galerkin adaptive mesh refinement (AMR) framework. The viscous term in the compressible Navier–Stokes equations is discretized using the high-order interior penalty discontinuous Galerkin (IPDG) method. In addition to the above, key numerical advancements encompass the rigorous derivation of the Lax–Friedrichs (L–F) numerical flux formulation tailored for moving mesh, an enhanced AMR-driven nodal correction methodology designed for curved surface geometries, and the implementation of a ghost-node boundary condition treatment scheme to address dynamic mesh motion. Numerical validation proceeds through three phases: first, the Couette flow simulations confirm the IPDG method's spatial convergence order. Subsequent analysis of an unsteady flow past a cylinder demonstrates the AMR framework's efficacy in resolving vortex-dominated flow. Finally, six VIV benchmark cases are simulated using the third-order IPDG discretization, establishing the proposed FSI approach's accuracy. Furthermore, synthetic jets (SJs) flow control is investigated through four frequency-variant SJs configurations. The results reveal that the SJs can achieve complete VIV suppression at a low actuation frequency, while higher actuation frequencies reduce suppression efficiency because the energy of the SJs is more in the form of acoustic waves.