A Multi-Scale Boltzmann Equation for Complex Systems of Neutral Gases across All Flow Regimes

TL;DR

This paper introduces a Multi-scale Boltzmann Equation derived from gas-kinetic theory, capable of modeling neutral gas flows across all regimes, validated through theoretical properties and numerical benchmarks.

Contribution

It presents a novel multi-scale Boltzmann Equation with variable observation time, bridging continuum and free-molecular flow regimes, and provides theoretical proofs and numerical validation.

Findings

The MBE accurately models flows across all regimes.

Theoretical properties like asymptotic behavior are established.

Numerical schemes validate the MBE against benchmark problems.

Abstract

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.