A systematic review of Lattice Boltzmann techniques for compressible flow modelling

Accurately extending the Lattice Boltzmann Method (LBM) to compressible flows remains non-trivial, owing to the strong compressibility introduces large density and temperature variations, steep gradients and shock discontinuities, and stringent stability requirements, while thermodynamic consistency and a robust treatment of the energy equation (and related transport properties) are not straightforward within standard formulations. The paper aims to provide a systematic review of LBM-based approaches for compressible flow simulations, conducted with PRISMA guidelines. 109 research papers from SCOPUS database, published between 2012 and 2024, were filtered by inclusion and exclusion criteria. The selected literature is analysed from both bibliometric and technical perspectives, including publication trends, journal and geographic distributions, and – more importantly – methodological strategies adopted to handle compressibility based on the flow regime. The manuscript highlights how the energy equation is addressed and evaluates the associated choices of collision operator and turbulence modelling, together with the reported Mach and Reynolds number and introduces summary tables acting as a decision-oriented practical guide for method selection. The findings indicate a strong acceleration of efforts after 2020 and a consolidation of research focus on the Mach 0.5–5 range, alongside clearer specialization in method selection for higher-speed regimes. In particular, current trends favour multi-speed lattices, Double Distribution Function (DDF) frameworks, and hybrid LBM–CFD couplings, often combined with advanced stabilization mechanisms (e.g. entropic or multi-relaxation formulations and high-resolution shock-capturing updates for energy transport) to improve robustness in presence of shocks. In conclusion, the review synthesizes the state of the art, clarifies the main modelling bottlenecks, and highlights open gaps motivating future developments towards stable, thermodynamically consistent, and computationally efficient LBM tools for high-speed compressible flow applications. The purpose is to help researchers to recognize relevant references useful for their specific interests and to identify the most used strategies based on flow regime, configuration, and LBM approach.