A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows III: Microflow Simulations (Communications in Computational Physics, 2013)
Due to the rapid advances in micro-electro-mechanical systems (MEMS), thestudy of microflows becomes increasingly important. Currently, the molecular-basedsimulation techniques are the most reliable methods for rarefied flow computation,even though these methods face statistical scattering problem in the low speed limit.With discretized particle velocity space, a unified gas-kinetic scheme (UGKS) for entire Knudsen number flow has been constructed recently for flow computation. Contrary to the particle-based direct simulation Monte Carlo (DSMC) method, the unifiedscheme is a partial differential equation-based modeling method, where the statisticalnoise is totally removed. But the common point between the DSMC and UGKS is thatboth methods are constructed through direct modeling in the discretized space. Dueto the multiscale modeling in the unified method, i.e., the update of both macroscopicflow variables and microscopic gas distribution function, the conventional constraintof time step being less than the particle collision time in many direct Boltzmann solversis released here. The numerical tests show that the unified scheme is more efficientthan the particle-based methods in the low speed rarefied flow computation. The mainpurpose of the current study is to validate the accuracy of the unified scheme in thecapturing of non-equilibrium flow phenomena. In the continuum and free molecularlimits, the gas distribution function used in the unified scheme for the flux evaluationat a cell interface goes to the corresponding Navier-Stokes and free molecular solutions. In the transition regime, the DSMC solution will be used for the validation ofUGKS results. This study shows that the unified scheme is indeed a reliable and accurate flow solver for low speed non-equilibrium flows. It not only recovers the DSMCresults whenever available, but also provides high resolution results in cases wherethe DSMC can hardly afford the computational cost. In thermal creep flow simulation,surprising solution, such as the gas flowing from hot to cold regions along the wall surface, is observed for the first time by the unified scheme, which is confirmed laterthrough intensive DSMC computation.