2024/06/11 by Sha Liu, Junzhe Cao, Liu, Sha +5 · 1 citation
Engineering · Mathematics · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies
paper · pdf · doi:10.48550/arxiv.2406.07038
openalex publication_date 2024/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Multi-scale Boltzmann Equation (MBE) is found from the gas-kinetic theory and the direct modeling philosophy as a master equation for complex physical systems of neutral gases across all flow regimes, which locates between the continuum limit and the free-molecular limit, covering a vast range of applications such as hypersonic flows over aerospace crafts and delicate flows around MEMS. The most explicit characteristic of MBE is evolving the variable observation time in the expression, which distinguishes the MBE from the single-scale master or governing equation where a fixed scale is implied in the assumptions. The fundamental properties of MBE, such as the asymptotic property, are proved theoretically, while a concise numerical scheme is developed for MBE to demonstrate its validity by benchmark multi-scale problems.