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基于第二粘性用局部微分求积法计算激波

赵勇 宗智 李章锐

赵勇, 宗智, 李章锐. 基于第二粘性用局部微分求积法计算激波[J]. 应用数学和力学, 2011, 32(3): 333-343. doi: 10.3879/j.issn.1000-0887.2011.03.009
引用本文: 赵勇, 宗智, 李章锐. 基于第二粘性用局部微分求积法计算激波[J]. 应用数学和力学, 2011, 32(3): 333-343. doi: 10.3879/j.issn.1000-0887.2011.03.009
ZHAO Yong, ZONG Zhi, LI Zhang-rui. Shock Calculation Based on Second Viscosity Using Localized Differential Quadrature Method[J]. Applied Mathematics and Mechanics, 2011, 32(3): 333-343. doi: 10.3879/j.issn.1000-0887.2011.03.009
Citation: ZHAO Yong, ZONG Zhi, LI Zhang-rui. Shock Calculation Based on Second Viscosity Using Localized Differential Quadrature Method[J]. Applied Mathematics and Mechanics, 2011, 32(3): 333-343. doi: 10.3879/j.issn.1000-0887.2011.03.009

基于第二粘性用局部微分求积法计算激波

doi: 10.3879/j.issn.1000-0887.2011.03.009
基金项目: 创新研究群体基金资助项目(50921001);国家973计划资助项目(2010CB832700)资助项目
详细信息
    作者简介:

    赵勇(1981- ),男,博士生(E-mail:fluid@mail.dlut.edu.cn);宗智(1964- )男,教授,博士(联系人.E-mail:zongzhi@dlut.edu.cn);李章锐(1985- ),男,博士生(E-mail:lizhangruix@yahoo.com.cn).

  • 中图分类号: O357

Shock Calculation Based on Second Viscosity Using Localized Differential Quadrature Method

  • 摘要: 考虑第二粘性效应,采用局部微分求积法数值求解激波问题.首先解释了在激波计算时,有必要考虑第二粘性,然后基于粘性模型,对一维和二维激波进行了数值模拟,还分别考察了剪切粘性力和第二粘性力对数值结果的影响.结果表明,采用粘性模型加上局部微分求积法能够模拟出激波特征,具有客观、简单的优点.
  • [1] Gary J. On certain finite difference schemes for hyperbolic systems[J]. Mathematics of Computation, 1964, 18(85):1-18.
    [2] Harten A. High resolution schemes for hyperbolic conservation laws[J].Journal of Computational Physics,1983,49:357-393. doi: 10.1016/0021-9991(83)90136-5
    [3] Harten A, Osher S. Uniformly high order accurate non-oscillatory schemes[J]. SIAM Journal on Numerical Analysis,1987, 24(2):279-309. doi: 10.1137/0724022
    [4] 张涵信.无波动、无自由参数的耗散差分格式[J].空气动力学学报,1988,6(2):143-164.(ZHANG Han-xin. Non-oscillatory and non-free-parameter dissipation difference scheme[J].Acta Aerodynamica Sinica, 1988, 6 (2):143-164.(in Chinese))
    [5] von Neumann J, Richtmyer R D. A method for the numerical calculation of hydrodynamic shocks[J]. Journal of Applied Physics, 1950, 21(3):232-237. doi: 10.1063/1.1699639
    [6] 袁湘江,周恒.计算激波的高精度数值方法[J].应用数学和力学,2000,21(5): 441-450.(YUAN Xiang-jiang, ZHOU Heng. Numerical schemes with high order of accuracy for the computation of shock wave[J].Applied Mathematics and Mechanics(English Edition),2000,21(5):489-500.)
    [7] 涂国华,袁湘江,陆利蓬.激波捕捉差分方法研究[J].应用数学和力学, 2007, 28(4): 433-439. (TU Guo-hua, YUAN Xiang-jiang, LU Li-peng. Developing shock-capturing difference methods[J]. Applied Mathematics and Mechanics(English Edition), 2007, 28(4):477-486.)
    [8] Bellman R E, Kashef B G, Casti J. Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations[J]. Journal of Computational Physics, 1972, 10(1):40-52. doi: 10.1016/0021-9991(72)90089-7
    [9] Shu C. Differential Quadrature and Its Applications in Engineering[M]. Springer: Berlin, 2000: 340-346.
    [10] Civian F, Sliepcevich C M. Differential quadrature for multidimensional problems[J]. Journal of Mathematical Analysis and Applications,1984, 101(2):423-443. doi: 10.1016/0022-247X(84)90111-2
    [11] Zong Z, Lam K Y. A localized differential quadrature method and its application to the 2D wave equation[J]. Computational Mechanics,2002, 29(4/5):382-391. doi: 10.1007/s00466-002-0349-4
    [12] Lam K Y, Zhang J, Zong Z A numerical study of wave propagation in a poroelastic medium by use of localized differential quadrature method[J]. Applied Mathematical Modelling, 2004, 28(5): 487-511.
    [13] Landau L D, Lifshitz E M. Fluid Mechanics[M].2nd Ed. Butterworth:Heinemann, 1999.
    [14] Stokes G G. On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids[J]. Transactions of the Cambridge Philosophical Society, 1845,8(22):287-342.
    [15] Vincenti W G, Kruger C H, Jr. Introduction to Physical Gas Dynamics[M]. Malabar, FL:Krieger, 1965: 407-412.
    [16] Anderson J D, Jr. Fundamentals of Aerodynamics[M]. New York: McGraw-Hill, 1984:649- 650.
    [17] Rick E G, Brian M A. Bulk viscosity: past to present[J]. Journal of Thermophysics and Heat Transfer,1999, 13(3):337-342. doi: 10.2514/2.6443
    [18] Sod G A. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws[J]. Journal of Computational Physics,1978, 27(1):1-31. doi: 10.1016/0021-9991(78)90023-2
    [19] Zong Z, Zhang Y Y. Advanced Differential Quadrature Methods[M]. Boca Raton: Chapman and Hall CRC Press, 2009: 189-208.
    [20] Samuel J M. Evaluating the second coefficient of viscosity from sound dispersion or absorption data[J]. AIAA Journal,Technical notes,1990, 28:171-173.
    [21] Toro E F. Riemann Solvers and Numerical Methods for Fluid Dynamics[M]. Berlin, Heidelberg:Springer, 1999:152-162.
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出版历程
  • 收稿日期:  2010-05-18
  • 修回日期:  2011-02-16
  • 刊出日期:  2011-03-15

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