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Volume 42 Issue 5
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LI Qibing, XU Kun. PROGRESS IN GAS-KINETIC SCHEME[J]. Advances in Mechanics, 2012, 42(5): 522-537. doi: 10.6052/1000-0992-11-149
Citation: LI Qibing, XU Kun. PROGRESS IN GAS-KINETIC SCHEME[J]. Advances in Mechanics, 2012, 42(5): 522-537. doi: 10.6052/1000-0992-11-149
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PROGRESS IN GAS-KINETIC SCHEME

doi: 10.6052/1000-0992-11-149
  • 1.

    School of Aerospace, Tsinghua University, Beijing 100084, China

  • 2. Department of Mathematics, Hong Kong University of Science and Technology, Kowloon, Hong Kong

Funds:  The project was supported by the National Natural Science Foundation of China (10872112, 11172154) and Hong Kong Research Grant Council (621709, 621011).
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  • Corresponding author: LI Qibing
  • Received Date: 2011-10-28
  • Rev Recd Date: 2012-06-08
  • Publish Date: 2012-09-25
    Abstract
  • Recent progress in the development of the gas-kinetic scheme is reviewed in this article, with emphasis laid on the construction of high-order-accurate gas-kinetic flux function for the Navier-Stokes equations and the unified gas-kinetic scheme for flow simulations in the entire Knudsen number regimes. A third-orderaccurate gas-kinetic scheme is presented through the high-order reconstruction of the initial data and the high-order gas evolution model of the gas distribution function. Different from traditional high-order schemes based on Riemann solution, the new scheme not only takes into account the high-order initial reconstruction at a cell interface, but also follows its time evolution, which ensures a high-order time accurate flux function. This study pioneers a new way to construct high accurate time-space coupling CFD method. The unified gaskinetic scheme for arbitrary Knudsen number is developed by direct solving the Boltzmann model equation in the discrete velocity space, where the update of both macroscopic conservative variables and microscopic gas distribution function takes place simultaneously within a time step. The newly developed method is more efficient than existing DVMs, where the continuum flow limit can be easily obtained in the unified scheme due to its hydrodynamic scale part of the flux function. The importance of using a valid physical evolution model in the construction of a numerical method is also discussed. The good performance of gas-kinetic scheme comes mainly from its capability of capturing a rational gas evolution process from an initial discontinuity using gas-kinetic model. The coupling of particle free transport and collision plays an important role here. Through the analysis of dissipative mechanism inside a numerical shock layer, it is realized that the adoption of exact Riemann solution of the Euler equations as a foundation of modern compressible CFD methods has fundamental flaws, and the shock instability at high Mach number simulation is unavoidable. The gas-kinetic scheme follows a valid physical process in the construction of numerical shock structure.

     

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