An Adaptive Mesh Refinement–Rotated Lattice Boltzmann Flux Solver for Numerical Simulation of Two and Three-Dimensional Compressible Flows with Complex Shock Structures

An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied to solve the flow filed by reconstructing the fluxes at each cell interface adaptively with the mesoscopic lattice Boltzmann model. To locally and dynamically improve the resolution of intricate shock structures and optimize the required computational resources, a block-structured adaptive mesh refinement (AMR) technique is introduced. The validity and effectiveness of the proposed method are confirmed through a range of two and three-dimensional numerical cases, including the shock tube problem, the four-wave Riemann problem, explosion within a rectangular box, and the vorticity induced by a shock. The results obtained using the AMR-RLBFS exhibit excellent agreement with published data and demonstrate high accuracy in capturing complex shock structures. The computational efficiency of the AMR-RLBFS can be also improved significantly compared to the RLBFS on uniform grids. Furthermore, the numerical outcomes underscore the capability of the AMR-RLBFS to eliminate shock instability effects while efficiently capturing a broader spectrum of small-scale vertical structures. These findings highlight the ability of AMR-RLBFS to improve the computational efficiency and capture intricate shock structures effectively, making it a valuable tool for studying a wide range of compressible flows from aerodynamics to astrophysics.