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A Numerical Method for Simulation of Microflows by Solving Directly Kinetic Equations with WENO Schemes

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Abstract

A numerical method for simulation of transitional-regime gas flows in microdevices is presented. The method is based on solving relaxation-type kinetic equations using high-order shock capturing weighted essentially non-oscillatory (WENO) schemes in the coordinate space and the discrete ordinate techniques in the velocity space. In contrast to the direct simulation Monte Carlo (DSMC) method, this approach is not subject to statistical scattering and is equally efficient when simulating both steady and unsteady flows. The presented numerical method is used to simulate some classical problems of rarefied gas dynamics as well as some microflows of practical interest, namely shock wave propagation in a microchannel and steady and unsteady flows in a supersonic micronozzle. Computational results are compared with Navier–Stokes and DSMC solutions.

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Acknowledgments

We are grateful to our colleagues Dr. Ye. Bondar for providing the results of his DSMC calculations and Dr. D. Khotyanovsky for his help with preparing the paper. This work has been supported by the Russian Academy of Sciences under the program “Fundamental problems of mechanics of interaction in technological and natural systems, materials and media” and by the Russian Foundation for Basic Research (RFBR Project No. 12-01-00776-a). This support is gratefully acknowledged

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  1. Laboratory of Computational Aerodynamics, Khristianovich Institute of Theoretical and Applied Mechanics, 630090 , Novosibirsk, Russia

    A. N. Kudryavtsev & A. A. Shershnev

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Kudryavtsev, A.N., Shershnev, A.A. A Numerical Method for Simulation of Microflows by Solving Directly Kinetic Equations with WENO Schemes. J Sci Comput 57, 42–73 (2013). https://doi.org/10.1007/s10915-013-9694-z

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