An Immersed Boundary-Lattice Boltzmann Method for Compressible Flows

Abstract: This study aims to develop and validate an efficient numerical method to investigate compressible flows in fluid-structure interaction scenarios, such as vortex-induced vibrations in a bluff body or flapping wings. Inspired by the simplicity and robustness of the lattice Boltzmann method (LBM), it has been extended to compressible flows involving fluid-structure interactions. Due to its intrinsic parallel nature, LBM stands at the forefront of solving many industrial problems when coupled with immersed boundary methods (IBM). However, the conventional scheme is still not well suited for high-speed flows., In this study, we developed a hybrid compressible LBM approach, using LBM for the mass and momentum equations and the finite difference method (FDM) for the energy equation, alongside a penalty IBM. The well-known Mach cubic error for high-speed flows is corrected using a forcing term along with penalty IB forces. Additionally, a hybrid recursive regularized collision model based on the pressure-based method is used to maintain accuracy and stability in highly compressible flows., For validation, subsonic and supersonic flow over a 2D circular cylinder, as well as transonic flow over a NACA airfoil, are presented. The current findings show good agreement with previously published data derived from alternative methodologies, validating the effectiveness of the proposed approach in simulating highly compressible flows. Keywords: Lattice Boltzmann method, Immersed-boundary method, Viscous compressible flows, Recursive regularized, Fluid-structure interaction, Shock waves, Computational fluid dynamics