Simulation Methods for Rarefied Gas Flows

Abstract

Low-speed gas flows of large Knudsen (Kn) number are characteristic of micro/nano-electro-mechanical systems (MEMS/NEMS), vacuum system and tight/shale gas reservoirs, and can be described by the kinetic theory. The traditional direct simulation Monte Carlo (DSMC) method is the standard technique for modeling gas flows at high Kn but computationally expensive and practically unfordable at low speed due to stochastic noise. The discrete velocity method (DVM) is another traditional method and deterministically solves the Boltzmann kinetic equation or its simplified model equations. It can produce noise-free results that are accurate when fine grid is used in the discretization of high-dimensional phase space, which generally requires high computational cost in terms of memory usage and CPU time. The direct simulation BGK (DSBGK) method was proposed recently to solve the BGK model equation and has been comprehensively validated against the DSMC method and experimental data in several benchmark problems over a wide range of Kn. Although it is also a particle-based approach like the DSMC method, its stochastic noise is very low and independent of the flow speed (or Mach number in general), which is in sharp contrast to the DSMC method, where the stochastic noise is inversely proportional to the square of Mach number. The algorithms of this three simulation methods are introduced in this chapter and several benchmark problems are studied to show their numerical performances in terms of accuracy, efficiency, memory usage, as well as robustness associated with algorithm simplicity.