Shock Waves (2011) 21:35–42 DOI 10.1007/s00193-010-0274-y ORIGINAL ARTICLE Shock compression of some porous media in conical targets: numerical study A. A. Charakhch’yan · K. V. Khishchenko · V. E. Fortov · A. A. Frolova · V. V. Milyavskiy · L. V. Shurshalov Received: 31 March 2009 / Revised: 5 October 2009 / Accepted: 24 April 2010 / Published online: 7 September 2010 © Springer-Verlag 2010 Abstract Axially symmetric flows in conical solid targets filled by porous aluminum, graphite or polytetrafluoroethyl- ene under impact of an aluminum plate with the velocity of 2.5 km/s are simulated numerically within the framework of the model of the hypoelastic ideal-plastic solid. The porosity of the samples is taken into account by conservation laws at the leading shock wave; the medium behind that is sup- posed to be nonporous. Equations of state for all materials in question are used to describe thermodynamic properties of the impactor and target over a wide range of pressures and temperatures taking into account phase transformations. The maximal over space and time pressure as a function of the initial relative density is presented and discussed. Keywords Porous media · Condensed media · Converging shock waves · Conical targets 1 Introduction In continuation of our study of the shock compression of graphite in conical targets [1, 2] we have taken into account the initial porosity of samples and discovered a significant increase in the peak (maximal over space and time) pressure by decreasing the initial density of graphite, which is quite different from a case of plane shock waves. This finding Communicated by N. Thadhani. A. A. Charakhch’yan (B ) · A. A. Frolova · L. V. Shurshalov Dorodnicyn Computing Centre, Russian Academy of Sciences, Vavilov St. 40, Moscow 119333, Russia e-mail: chara@ccas.ru K. V. Khishchenko · V. E. Fortov · V. V. Milyavskiy Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya St. 13, Bd. 2, Moscow 125412, Russia stimulated the study of mathematical problems describ- ing flows of initially porous condensed media with con- verging shock waves. Both spherical and cylindrical 1D shock waves as well as some flows in conical targets were considered [3–6]. The shock wave in a porous condensed medium is consid- ered [7] as a discontinuity; the matter behind that is nonpo- rous and described using the hydrodynamics equations and the equations of state P = P (ρ, T ), ε = ε(ρ, T ), (1) where P is the pressure, ρ is the density, T is the tempera- ture, and ε is the specific internal energy. The shock velocity and the unknown functions of the hydrodynamics equations at the shock front are related by conservation laws for the mass, momentum, and energy. Such a simple model, which takes into account the poros- ity only in the boundary condition for the hydrodynamic equations fails to explain a lot of measurements, such as the experiment with essentially inhomogeneous heating of a substance in a shock wave [8] and the shock-tube measure- ments with bubbly liquids [9]. Nevertheless, if dimensions of pores are sufficiently small and the shock wave is sufficiently strong, the approach based on the conservation laws may be applicable to converging shock waves, as well as it is applica- ble to the interpretation of experimental data in determining the Hugoniot of porous media. A simple model of a deformable solid is used in this work to take into account shear stresses (see Sect. 2). The numeri- cal method for hydrodynamic flows with moving internal and external boundaries (see, e.g., [10]) was generalized in [5] for the model. The conservation laws for the mass, momen- tum, and energy through the leading shock wave are satisfied due to a conservative form of finite-difference schemes for the equations. Details of the numerical method relating to 123