Abstract
In present paper, I have studied second-kind self-similar solutions of converging cylindrical shock wave in non-ideal magnetogasdynamics. Two trial functions suggested by Singh et al. and the shooting method of Landau–Stanyukovich are used to determine the similarity exponent α for different values of specific heat ratio γ and the parameter k, where k∈(0,1] and internal volume \(\tilde{b}\) in non-ideal magnetogasdynamics.
Similar content being viewed by others
References
Butler, D.: Converging spherical and cylindrical shocks. Armament Res. Estab. Rep. (1954)
Chisnell, R.F.: J. Fluid Mech. 354, 357 (1998)
Guderley, G.: Luftfahrtforschung 19, 302 (1942)
Gurovich, V.Ts., Fel, L.G.: J. Exp. Theor. Phys. 89(1), 14 (2009)
Gurovich, V.Ts., Grinenko, A., Krasik, Y.E.: Phys. Rev. Lett. 4, 124503 (2007)
Hafner, P.: SIAM J. Appl. Math. 48, 1244 (1988)
Hirschler, T., Gretler, W.: Z. Angew. Math. Phys. 52, 151 (2001)
Lazarus, R.B.: SIAM J. Numer. Anal. 18, 316 (1981)
Radha, Ch., Sharma, V.D.: Phys. Fluids B 5, 4287 (1993)
Sedov, L.I.: Similarity and Dimensional Methods in Mechanics. Academic Press, New York (1959)
Singh, L.P., Singh, M., Pandey, B.D.: AIAA J. 48(11), 2523 (2010a)
Singh, L.P., Husain, A., Singh, M.: Chin. Phys. Lett. 27(1), 014702 (2010b)
Singh, M., Singh, L.P., Husain, A.: Chin. Phys. Lett. 28(9), 094701 (2011a)
Singh, L.P., Husain, A., Singh, M.: Meccanica 46(2), 437 (2011b)
Singh, L.P., Singh, M., Husain, A.: Astrophys. Space Sci. 331, 597 (2011c)
Stanyukovich, K.P.: Unsteady Motion of Continuous Media. Pergamon, New York (1960)
Taylor, M.G.G.T., Cargill, P.J.: J. Plasma Phys. 66, 239 (2001)
Toque, N.: Shock Waves 11, 157 (2001)
Welsh, R.L.: J. Fluid Mech. 29, 61 (1967)
Whitham, G.B.: Linear and Nonlinear Waves. Interscience, New York (1974)
Zeldovich, Y.B., Raizer, Y.P.: Physics of Shock Waves and High Temperature Hydrodynamic Phenomenon II. Academic Press, New York (1967)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Singh, M. Similarity parameters for converging shock waves in non-ideal magnetogasdynamics by Landau-Stanyukovich rule. Astrophys Space Sci 343, 615–619 (2013). https://doi.org/10.1007/s10509-012-1262-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-012-1262-8