Analytical Solutions of Shock Structure Thickness and Asymmetry in Navier–Stokes/Fourier Framework

No AccessTechnical NoteAnalytical Solutions of Shock Structure Thickness and Asymmetry in Navier–Stokes/Fourier FrameworkR. S. MyongR. S. MyongDepartment of Aerospace and System Engineering and Research Center for Aircraft Parts Technology, Gyeongsang National University, Gyeongnam 660-701, Republic of KoreaPublished Online:22 Apr 2014https://doi.org/10.2514/1.J052583SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations About References [1] Becker R., "Stosswelle und Detonation," Zeitschrift für Physik, Vol. 8, No. 1, 1922, pp. 321–362. CrossrefGoogle Scholar[2] Taylor G. I. and Maccoll J. W., "Mechanics of Compressible Fluids," Aerodynamics Theory, Durand W. F. (ed.), Vol. 3, Springer, Berlin, 1934. Google Scholar[3] Morduchow M. and Libby P. A., "On a Complete Solution of the One-Dimensional Flow Equations of a Viscous, Heat-Conducting, Compressible Gas," Journal of the Aeronautical Sciences, Vol. 16, No. 11, 1949, pp. 674–684, 704. JASCAR 0095-9812 Google Scholar[4] Mott-Smith H. M., "Solution of the Boltzmann Equation of a Shock Wave," Physical Review, Vol. 82, No. 6, 1951, pp. 885–892. doi:https://doi.org/10.1103/PhysRev.82.885 PHRVAO 0031-899X CrossrefGoogle Scholar[5] Grad H., "Profile of a Steady Plane Shock Wave," Communication on Pure and Applied Mathematics, Vol. 5, No. 3, 1952, pp. 257–300. doi:https://doi.org/10.1002/cpa.3160050304 CrossrefGoogle Scholar[6] Al-Ghoul M. and Eu B. C., "Generalized Hydrodynamics and Shock Waves," Physical Review E, Vol. 56, No. 3, 1997, pp. 2981–2992. doi:https://doi.org/10.1103/PhysRevE.56.2981 PLEEE8 1063-651X CrossrefGoogle Scholar[7] Myong R. S., "Thermodynamically Consistent Hydrodynamic Computational Models for High-Knudsen-Number Gas Flows," Physics of Fluids, Vol. 11, No. 9, 1999, pp. 2788–2802. CrossrefGoogle Scholar[8] Josyula E., Vedula P. and Bailey W. F., "Kinetic Solution of Shock Structure in a Non-Reactive Gas Mixture," AIAA Paper 2010-817, 2010. LinkGoogle Scholar[9] Liepmann H. W. and Roshko A., Elements of Gasdynamics, Wiley, New York, 1957. CrossrefGoogle Scholar[10] Vincenti W. G. and Kruger C. H., Introduction to Physical Gas Dynamics, Wiley, New York, 1967. Google Scholar[11] Gombosi T. I., Gaskinetic Theory, Cambridge Univ. Press, New York, 1994. CrossrefGoogle Scholar[12] Gilbarg D. and Paolucci D., "Structure of Shock Waves in the Continuum Theory of Fluids," Journal of Rational Mechanics and Analysis, Vol. 2, No. 4, 1953, pp. 617–642. doi:https://doi.org/10.1512/iumj.1953.2.52031 Google Scholar[13] Schmidt B., "Electron Beam Density Measurements in Shock Waves in Argon," Journal of Fluid Mechanics, Vol. 39, No. 2, 1969, pp. 361–366. doi:https://doi.org/10.1017/S0022112069002229 JFLSA7 0022-1120 CrossrefGoogle Scholar[14] Alsmeyer H., "Density Profiles in Argon and Nitrogen Shock Waves Measured by the Absorption of an Electron Beam," Journal of Fluid Mechanics, Vol. 74, No. 3, 1976, pp. 497–513. doi:https://doi.org/10.1017/S0022112076001912 JFLSA7 0022-1120 CrossrefGoogle Scholar[15] Boyd I. D., "Analysis of Rotational Non-Equilibrium in Standing Shock Waves of Nitrogen," AIAA Journal, Vol. 28, No. 11, 1990, pp. 1997–1999. doi:https://doi.org/10.2514/3.10511 AIAJAH 0001-1452 LinkGoogle Scholar[16] Zhong X., MacCormack R. W. and Chapman D. R., "Stabilization of the Burnett Equations and Applications to Hypersonic Flows," AIAA Journal, Vol. 31, No. 6, 1993, pp. 1036–1043. doi:https://doi.org/10.2514/3.11726 AIAJAH 0001-1452 LinkGoogle Scholar[17] Woo M. and Greber I., "Molecular Dynamics Simulation of Piston-Driven Shock Wave in Hard Sphere Gas," AIAA Journal, Vol. 37, No. 2, 1999, pp. 215–221. doi:https://doi.org/10.2514/2.692 AIAJAH 0001-1452 LinkGoogle Scholar[18] Xu K., "Gas-Kinetic BGK Scheme for the Navier–Stokes Equations and Its Connection with Artificial Dissipation and Godunov Method," Journal of Computational Physics, Vol. 171, No. 1, 2001, pp. 289–335. doi:https://doi.org/10.1006/jcph.2001.6790 JCTPAH 0021-9991 CrossrefGoogle Scholar[19] Myong R. S., "Computational Method for Eu's Generalized Hydrodynamic Equations of Rarefied and Microscale Gasdynamics," Journal of Computational Physics, Vol. 168, 2001, pp. 47–72. doi:https://doi.org/10.1006/jcph.2000.6678 JCTPAH 0021-9991 CrossrefGoogle Scholar[20] Myong R. S., "Generalized Hydrodynamic Computational Model for Rarefied and Microscale Diatomic Gas Flows," Journal of Computational Physics, Vol. 195, No. 2, 2004, pp. 655–676. doi:https://doi.org/10.1016/j.jcp.2003.10.015 JCTPAH 0021-9991 CrossrefGoogle Scholar[21] Cai C., Liu D. D. and Xu K., "One-Dimensional Multiple-Temperature Gas-Kinetic Bhatnagar Gross Krook Scheme for Shock Wave Computation," AIAA Journal, Vol. 46, No. 5, 2008, pp. 1054–1062. doi:https://doi.org/10.2514/1.27432 AIAJAH 0001-1452 LinkGoogle Scholar[22] Iannelli J., "Implicit Galerkin Finite Element Runge–Kutta Algorithm for Shock Structure Investigations," Journal of Computational Physics, Vol. 230, No. 1, 2011, pp. 260–286. doi:https://doi.org/10.1016/j.jcp.2010.09.025 JCTPAH 0021-9991 CrossrefGoogle Scholar[23] Roy C. J., McWherter-Payne M. A. and Oberkampf W. L., "Verification and Validation for Laminar Hypersonic Flowfields, Part 1: Verification," AIAA Journal, Vol. 41, No. 10, 2003, pp. 1934–1943. doi:https://doi.org/10.2514/2.1909 AIAJAH 0001-1452 LinkGoogle Scholar[24] Fogiel M., Handbook of Mathematical, Scientific, and Engineering: Formulas, Tables, Functions, Graphs, Transforms, Research and Education Assoc., NJ, 1997. Google Scholar Previous article Next article