Hybrid Immersed Boundary-Lattice Boltzmann Method for Compressible Flows*

This talk presents a numerical method for simulating compressible flows using a penalty immersed-boundary method (IBM) coupled with the lattice Boltzmann method (LBM). The LBM has become a popular alternative to conventional numerical methods due to its ease of implementation and lower computational cost. Because of its intrinsic parallel nature, it stands at the forefront of solving many industrial problems when coupled with IBM. However, traditional LBM struggles with high-speed flows due to the inability of standard lattice models to recover the compressible Navier-Stokes equations. 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 an iterative IBM. To guarantee accuracy and stability, a 4th-order hybrid recursive regularized collision model has been adopted. The errors in the stress tensor of standard LBM for high-speed flows are corrected using a numerical force. A diffuse IBM is adopted due to its better numerical efficiency in handling moving geometries and because it can also handle thermal boundary conditions. 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 current solver in simulating highly compressible flows.