Simulations of Micro Channel Gas Flows with Domain Decomposition Technique for Kinetic and Fluid Dynamics Equations

摘要

In the last 20 years many research papers have been reported about the development of domain decompositions for the kinetic and the fluid dynamic equations, see for example. From large to small scale geometries one may experience different degrees of rarefaction of a gas. The degrees of rarefaction of a gas can be measured by the Knudsen number Kn = λ/L, where λ is the mean free path and L is the characteristic length, for example the channel width. For Kn ＜ 0.001, the flow is in the continuum regime, the compressible Navier-Stokes equations with no-slip boundary conditions are solved. For 0.001 ＜ Kn ＜ 0.1, the flow is in the slip regime, where the Navier-Stokes equations with velocity-slip and temperature jump conditions are solved. For Kn ＞ 0.1 a kinetic type approach, based on the Boltzmann equation is required. We note that the kinetic approach is valid in the whole range of rarefaction of a gas. At standard conditions the mean free path of a gas in a micro- or nano channel is of the order L or larger, so the Knudsen number is no longer small. Therefore, the fluid dynamic equations, the compressible Euler or Navier-Stokes equations, cannot predict the flows correctly in a small scale geometry.