LI Zhi-hui, BI Lin, TANG Zhi-gong. Study of Gas-Kinetic Numerical Schemes for One-and Two-Dimensional Inner Flows[J]. Applied Mathematics and Mechanics, 2009, 30(7): 833-846. doi: 10.3879/j.issn.1000-0887.2009.07.008
Citation: LI Zhi-hui, BI Lin, TANG Zhi-gong. Study of Gas-Kinetic Numerical Schemes for One-and Two-Dimensional Inner Flows[J]. Applied Mathematics and Mechanics, 2009, 30(7): 833-846. doi: 10.3879/j.issn.1000-0887.2009.07.008

Study of Gas-Kinetic Numerical Schemes for One-and Two-Dimensional Inner Flows

doi: 10.3879/j.issn.1000-0887.2009.07.008
  • Received Date: 2008-10-17
  • Rev Recd Date: 2009-05-27
  • Publish Date: 2009-07-15
  • Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions were designed with different-order precision by analyzing the inner characteristic of the gas-kinetic numerical algorithm for Boltzmann model equation.The peculiar flow phenomena and mechanism from various flow regimes were revealed by the numerical simulation of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers,and the numerical remainde-reffects of the difference schemes were investigated and analyzed on computed results.The ways of improving the computational efficiency of the gas-kinetic numerical method and the computing principles of difference discretization were discussed on the Boltzmann model equation.
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  • [1]
    Sod G A. A survey of several finite difference methods for systems of non-linear hyperbolic conservation laws[J].Journal of Computational Physics,1978,27(1):1-31. doi: 10.1016/0021-9991(78)90023-2
    [2]
    Chu C K. Kinetic-theoretic description of the formation of a shock wave[J].Physics of Fluids,1965,8(1):12-22. doi: 10.1063/1.1761077
    [3]
    Reitz R D. One-dimensional compressible gas dynamics calculations using the Boltzmann equations[J].Journal of Computational Physics,1981,42(1):108-123. doi: 10.1016/0021-9991(81)90235-7
    [4]
    Shu C W, Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes Ⅰ[J].Journal of Computational Physics,1988,77(2):439-471. doi: 10.1016/0021-9991(88)90177-5
    [5]
    Gorelov S L, Kogan M N. Solution of linear problem of rarefied gas dynamics by the Monte Carlo method[J].Fluid Dynamics,1968,3(2):96-98.
    [6]
    Huang A B, Hwang P F. Test of statistical models for gases with and without internal energy states[J].Physics of Fluids,1973,16(4):466-575. doi: 10.1063/1.1694368
    [7]
    Alofs D J, Flagan R C, Springer G S.Density distribution measurements in rarefied gases contained between parallel plates at high temperature differences[J].Physics of Fluids,1971,14(3):529-533. doi: 10.1063/1.1693466
    [8]
    Tritton D J.Physical Fluid Dynamics[M].Oxford:Oxford University Press, 1988.
    [9]
    Prendergast K H, Xu K. Numerical hydrodynamics from gas-kinetic theory[J].Journal of Computational Physics,1993,109(1):53-66. doi: 10.1006/jcph.1993.1198
    [10]
    Yang J Y, Huang J C. Rarefied flow computations using nonlinear model Boltzmann equations[J].Journal of Computational Physics,1995,120(2):323-339. doi: 10.1006/jcph.1995.1168
    [11]
    Zheng Y, Garcia A L, Alder B J. Comparison of kinetic theory and hydrodynamics for poiseuille flow[J].Journal of Statistical Physics,2002,109(3/4):495-505. doi: 10.1023/A:1020498111819
    [12]
    Luo L S, Chen H, Chen S,et al.Generalized hydrodynamic transport in lattice gas automata[J].Physical Review A,1991,43(12):7097-7100. doi: 10.1103/PhysRevA.43.7097
    [13]
    Chen S, Doolen G D. Lattice Boltzmann method for fluid flows[J].Annual Review of Fluid Mechanics,1998,30(1):329-364. doi: 10.1146/annurev.fluid.30.1.329
    [14]
    Sone Y, Takata S, Ohwada T. Numerical analysis of the plane Couette flow of a rarefied gas on the basis of the linearized Boltzmann equation for hard-sphere molecules[J].European Journal of Mechanics-B/Fluids,1990,9(3):449-456.
    [15]
    Xu K, Li Z H. Microchannel flow in the slip regime:gas-kinetic BGK-Burnett solutions[J].Journal of Fluid Mechanics,2004,513:87-110. doi: 10.1017/S0022112004009826
    [16]
    李志辉. 从稀薄流到连续流的气体运动论统一数值算法研究[D].博士论文. 四川绵阳:中国空气动力研究与发展中心研究生部, 2001.
    [17]
    Li Z H, Zhang H X. Numerical investigation from rarefied flow to continuum by solving the Boltzmann model equation[J].International Journal of Numerical Methods in Fluids,2003,42(4):361-382. doi: 10.1002/fld.517
    [18]
    Li Z H, Zhang H X. Study on gas kinetic unified algorithm for flows from rarefied transition to continuum[J].Journal of Computational Physics,2004,193(2):708-738. doi: 10.1016/j.jcp.2003.08.022
    [19]
    Li Z H, Zhang H X. Gas-kinetic description of shock wave structures by solving Boltzmann model equation[J].International Journal of Computational Fluid Dynamics, 2008,22(9):623-638. doi: 10.1080/10618560802395117
    [20]
    Zhang H X, Zhuang F G.NND Schemes and Their Applications to Numerical Simulation of Two- and Three-Dimensional Flows[M].In:Hutchinson J W,Wu T Y,Eds.Advances in Applied Mechanics.29.Holland:Academic Press,1992,193-256.
    [21]
    Shizgal B. A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems[J].Journal of Computational Physics,1981,41(2):309-328. doi: 10.1016/0021-9991(81)90099-1
    [22]
    Yee H C. Construction of explicit and implicit symmetric TVD schemes and their applications[J].Journal of Computational Physics,1987,68(1):151-179. doi: 10.1016/0021-9991(87)90049-0
    [23]
    张涵信, 沈孟育. 计算流体力学――差分方法的原理和应用[M].北京:国防工业出版社, 2003.
    [24]
    刘儒勋, 舒其望. 计算流体力学的若干新方法[M].北京:科学出版社,2003.
    [25]
    Schlichting H.Boundary-Layer Theory[M].Chap XII. New York:McGraw-Hill, 1968.
    [26]
    Nance R P, Hash D B, Hassan H A. Role of boundary conditions in Monte Carlo simulation of microelectromechanical systems[J].Journal of Thermophysics and Heat Transfer,1998,12(3):447-449. doi: 10.2514/2.6358
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