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.

# Shock Calculation Based on Second Viscosity Using Localized Differential Quadrature Method

##### doi: 10.3879/j.issn.1000-0887.2011.03.009
• Received Date: 2010-05-18
• Rev Recd Date: 2011-02-16
• Publish Date: 2011-03-15
• Based on the second viscosity,localized differential quadrature (LDQ) method was applied to solve shock tube problems.Firstly,the necessity was explained to consider the second viscosity to calculate shocks,then shock tubes based on the viscosity model were simulated,and finally,the roles of shear viscous stress and the second viscous stress were checked.The results show that the viscosity model combined with LDQ method can capture the main characters of shock and have the advantages of objectivity and simplicity.
•  [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. [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. [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. [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. [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. [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. [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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