Shock waves and explosions

Contents Preface ix Acknowledgements x 1 Introduction 1 2 The Piston Problem 15 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 The Piston Problem: Its Connection with the Blast Wave . . 17 2.3 Piston Problem in the Phase Plane . . . . . . . . . . . . . . . 23 2.4 Cauchy Problem in Relation to Automodel Solutions of One-Dimensional Nonsteady Gas Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5 Uniform Expansion of a Cylinder or Sphere into Still Air: An Analytic Solution of the Boundary Value Problem . . . . . . 33 2.6 Plane Gas Dynamics in Transformed Co-ordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3 The Blast Wave 49 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2 Approximate Analytic Solution of the Blast Wave Problem Involving Shocks of Moderate Strength . . . . . . . . . . . . . 56 3.3 Blast Wave in Lagrangian Co-ordinates . . . . . . . . . . . . 79 3.4 Point Explosion in an Exponential Atmosphere . . . . . . . . 90 3.5 Asymptotic Behaviour of Blast Waves at a High Altitude . . 99 3.6 Strong Explosion into a Power Law Density Medium . . . . . 103 3.7 Strong Explosion into Power Law Nonuniform Medium: Selfsimilar Solutions of the Second Kind . . . . . . . . . . . . . . 110 3.8 Point Explosion with Heat Conduction . . . . . . . . . . . . . 118 3.9 The Blast Wave at a Large Distance . . . . . . . . . . . . . . 130 vii © 2004 by Chapman & Hall/CRC viii Contents 4 Shock Propagation Theories: Some Initial Studies 137 4.1 Shock Wave Theory of Kirkwood and Bethe . . . . . . . . . . 137 4.2 The Brinkley-Kirkwood Theory . . . . . . . . . . . . . . . . . 144 4.3 Pressure Behind the Shock: A Practical Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 5 Some Exact Analytic Solutions of Gasdynamic Equations Involving Shocks 153 5.1 Exact Solutions of Spherically Symmetric Flows in Eulerian Co-ordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 5.2 Exact Solutions of Gasdynamic Equations in Lagrangian Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 5.3 Exact Solutions of Gasdynamic Equations with Nonlinear Particle Velocity . . . . . . . . . . . . . . . . . . . . . . . . . 170 6 Converging Shock Waves 177 6.1 Converging Shock Waves: The Implosion Problem . . . . . 177 6.2 Spherical Converging Shock Waves: Shock Exponent via the Pressure Maximum . . . . . . . . . . . . . . 183 6.3 Converging Shock Waves Caused by Spherical or Cylindrical Piston Motions . . . . . . . . . . . . . . . . . . . . . . . . . . 188 7 Spherical Blast Waves Produced by Sudden Expansion of a High Pressure Gas 195 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 7.2 Expansion of a High Pressure Gas into Air: A Series Solution . . . . . . . . . . . . . . . . . . . . . . . . 197 7.3 Blast Wave Caused by the Expansion of a High Pressure Gas Sphere: An Approximate Analytic Solution . . . . . . . 208 8 Numerical Simulation of Blast Waves 225 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 8.2 A Brief Review of Dierence Schemes for Hyperbolic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 8.3 Blast Wave Computations via Articial Viscosity . . . . 233 8.4 Converging Cylindrical Shock Waves . . . . . . . . . . . . . . 242 8.5 Numerical Simulation of Explosions Using Total Variation Diminishing Scheme . . . . . . . . . . . . . . . . . . . . . . . 253 References 265 © 2004