Piston driven shock waves in non-homogeneous planar media

Abstract

In this work, we analyze in detail the problem of piston driven shock waves in planar media. Similarity solutions to the compressible hydrodynamics equations are developed, for a strong shock wave, generated by a time dependent pressure piston, propagating in a non-homogeneous planar medium consisting of an ideal gas. Power law temporal and spatial dependency is assumed for the piston pressure and initial medium density, respectively. The similarity solutions are written in both Lagrangian and Eulerian coordinates. It is shown that the solutions take various qualitatively different forms according to the value of the pressure and density exponents. We show that there exist different families of solutions for which the shock propagates at constant speed, accelerates or slows down. Similarly, we show that there exist different types of solutions for which the density near the piston is either finite, vanishes or diverges. Finally, we perform a comprehensive comparison between the planar shock solutions and Lagrangian hydrodynamic simulations, by setting proper initial and boundary conditions. A very good agreement is reached, which demonstrates the usefulness of the analytic solutions as a code verification test problem.

References in corpus (17)

• Theories of Gamma-Ray Bursts
• The Structure & Dynamics of Massive Early-type Galaxies: On Homology, Isothermality and Isotropy inside one Effective Radius
• Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing
• On Validating an Astrophysical Simulation Code
• Trans-Relativistic Blast Waves in Supernovae as Gamma-Ray Burst Progenitors
• Similarity Properties and Scaling Laws of Radiation Hydrodynamic Flows in Laboratory Astrophysics
• Non-relativistic radiation mediated shock breakouts: II. Bolometric properties of SN shock breakout
• Non-relativistic radiation mediated shock breakouts: I. Exact bolometric planar breakout solutions
• Non-relativistic radiation mediated shock breakouts: III. Spectral properties of SN shock breakout
• Converging Shock Flows for a Mie-Grüneisen Equation of State
• The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas
• Full self-similar solutions of the subsonic radiative heat equations
• Revisiting the Strong Shock Problem: Converging and Diverging Shocks in Different Geometries
• Analytic solutions of the nonlinear radiation diffusion equation with an instantaneous point source in non-homogeneous media
• Self-similar solution of the subsonic radiative heat equations using a binary equation of state
• Solutions of the imploding shock problem in a medium with varying density
• Radiation drive temperature measurements in aluminium via radiation-driven shock waves: Modeling using self-similar solutions

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