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: Self-similar Solutions of the Second Kind ....................... 110 3.8 Point Explosion with Heat Conduction ............................ 118 3.9 The Blast Wave at a Large Distance .............................. 130 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 Co-ordinates .................................................... 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 Difference Schemes for Hyperbolic Systems ..... 228 8.3 Blast Wave Computations via Artificial Viscosity ................ 233 8.4 Converging Cylindrical Shock Waves .............................. 242 8.5 Numerical Simulation of Explosions Using Total Variation Diminishing Scheme .............................................. 253 References ............................................................ 265 Index ................................................................. 275