A multiscale Boltzmann equation for complex systems of neutral gases across all flow regimes

A multiscale Boltzmann equation (MBE) is found from the gas-kinetic theory as the master equation for complex physical systems of neutral gases across all flow regimes, which span from the continuum limit to the free-molecular limit, covering a vast range of applications such as hypersonic flows over near-space vehicles and delicate flows around micro-electromechanical systems. A key feature of this MBE is the introduction of the observation scale into the master equation, which distinguishes the MBE from single-scale master (or governing) equations where fixed observation scales are implied in their basic assumptions. The fundamental properties of MBE, such as the asymptotic preserving property, are proved theoretically, and a concise numerical scheme is developed for MBE to demonstrate its validity on benchmark multiscale problems.