The numerical instability of the lattice Boltzmann method (LBM) at high Mach or high Reynolds number flow is well identified, and it remains a major barrier to its application in more complex configurations such as moving geometries. This work combines the compressible lattice Boltzmann model with rotating overset grids (the so-called Chimera method, sliding mesh, or moving reference frame) for high Mach flows. This paper proposes to use the compressible hybrid recursive regularized collision model with fictitious forces (or inertial forces) in a noninertial rotating reference frame. Also, polynomial interpolations are investigated, which allow fixed inertial and rotating noninertial grids to communicate with each other. We suggest a way to effectively couple the LBM with the MUSCL-Hancock scheme in the rotating grid, which is needed to account for thermal effect of compressible flow. As a result, this approach is demonstrated to have an extended Mach stability limit for the rotating grid. It also demonstrates that this complex LBM scheme can maintain the second-order accuracy of the classic LBM by appropriately using numerical methods like polynomial interpolations and the MUSCL-Hancock scheme. Furthermore, the method shows a very good agreement on aerodynamic coefficients compared to experiments and the conventional finite-volume scheme. This work presents a thorough academic validation and error analysis of the LBM for simulating moving geometries in high Mach compressible flows.

• Received 10 November 2022
• Accepted 6 April 2023

DOI:https://doi.org/10.1103/PhysRevE.107.045306