GPU-based compressible lattice Boltzmann simulations on non-uniform grids using standard C++ parallelism: From best practices to aerodynamics, aeroacoustics and supersonic flow simulations

Despite decades of research, creating accurate, robust, and efficient lattice Boltzmann methods (LBM) on non-uniform grids with seamless GPU acceleration remains challenging. This work introduces a novel strategy to address this challenge by integrating simple yet effective components: (1) parallel algorithms in modern C++, (2) conservative cell-centered grid refinement, (3) local boundary conditions, and (4) robust collision models. Our framework supports multiple lattices (D2Q9, D2Q13, D2Q21, D2Q37, D3Q27, etc) tailored to various flow conditions. It includes collision models with polynomial and numerical equilibria, a second distribution for polyatomic behavior, a Jameson-like shock sensor, and generalizes Rohde's refinement strategy.

The framework's accuracy and robustness is validated across diverse benchmarks, including lid-driven cavity flows, Aeolian noise, 30P30N airfoil aerodynamics, inviscid Riemann problems, and viscous flows past a NACA airfoil in transonic and supersonic regimes. Modern C++ further enables our framework to reach GPU-native performance, while ensuring high portability, modularity, and ease of implementation. Notably, weakly compressible LBMs achieve state-of-the-art GPU efficiency on non-uniform grids, while fully compressible LBMs benefit from acceleration equivalent to thousands of CPU cores in the most compute-intensive cases. Our advanced performance models incorporate neighbor-list and asynchronous time-stepping effects, providing new insights into the performance decomposition of LB simulations on non-uniform grids.

Overall, this study sets a new standard for portable, tree-based LBMs, demonstrating that a combination of well-chosen components can achieve high performance, accuracy, and robustness across various flow conditions. As a final proof-of-concept, adaptive mesh refinement is proposed for subsonic and supersonic applications.