Commun. Comput. Phys., 14 (2013), pp. 1147-1173.

A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows III: Microflow Simulations

Juan-Chen Huang 1, Kun Xu 2*, Pubing Yu 2

1 Department of Merchant Marine, National Taiwan Ocean University, Keelung 20224, Taiwan.
2 Mathematics Department, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.

Received 19 September 2012; Accepted (in revised version) 8 February 2013
Available online 13 June 2013


Due to the rapid advances in micro-electro-mechanical systems (MEMS), the study of microflows becomes increasingly important. Currently, the molecular-based simulation 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 unified scheme is a partial differential equation-based modeling method, where the statistical noise is totally removed. But, the common point between the DSMC and UGKS is that both methods are constructed through direct modeling in the discretized space. Due to the multiscale modeling in the unified method, i.e., the update of both macroscopic flow variables and microscopic gas distribution function, the conventional constraint of time step being less than the particle collision time in many direct Boltzmann solvers is released here. The numerical tests show that the unified scheme is more efficient than the particle-based methods in the low speed rarefied flow computation. The main purpose of the current study is to validate the accuracy of the unified scheme in the capturing of non-equilibrium flow phenomena. In the continuum and free molecular limits, the gas distribution function used in the unified scheme for the flux evaluation at 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 of UGKS 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 DSMC results whenever available, but also provides high resolution results in cases where the 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 later through intensive DSMC computation.

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PACS: 51.10.+y, 47.11.-j, 47.11.St, 47.45.-n
Key words: Unified scheme, non-equilibrium microflow, thermal creep flows.

*Corresponding author.
Email: (J.-C. Huang), (K. Xu), (P. B. Yu)

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