Shock Waves & Explosions

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ISBN: 9781584884224 | 1584884223
Cover: Hardcover
Copyright: 6/11/2004

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Understanding the causes and effects of explosions is important to experts in a broad range of disciplines, including the military, industrial and environmental research, aeronautic engineering, and applied mathematics. While offering an introductory review of historic research, Shock Waves & Explosions brings analytic and computational methods to a wide audience in a clear and thorough way. Beginning with an overview of the research on combustion and gas dynamics by Korobeinikov and Zeldovich in the 1970s and 1980s, the author brings readers up to date by covering modeling techniques and asymptotic and perturbative methods and ending with a chapter on computational methods.

Preface

Acknowledgements

1 Introduction

(14)

2 The Piston Problem

(34)

2.1 Introduction

(2)

2.2 The Piston Problem: Its Connection with the Blast Wave

(6)

2.3 Piston Problem in the Phase Plane

(5)

2.4 Cauchy Problem in Relation to Automodel Solutions of One-Dimensional Nonsteady Gas Flows

(5)

2.5 Uniform Expansion of a Cylinder or Sphere into Still Air: An Analytic Solution of the Boundary Value Problem

(4)

2.6 Plane Gas Dynamics in Transformed Co-ordinates

(12)

3 The Blast Wave

(88)

3.1 Introduction

(7)

3.2 Approximate Analytic Solution of the Blast Wave Problem Involving Shocks of Moderate Strength

(23)

3.3 Blast Wave in Lagrangian Co-ordinates

(11)

3.4 Point Explosion in an Exponential Atmosphere

(9)

3.5 Asymptotic Behaviour of Blast Waves at a High Altitude

(4)

3.6 Strong Explosion into a Power Law Density Medium

103

(7)

3.7 Strong Explosion into Power Law Nonuniform Medium: Self-similar Solutions of the Second Kind

110

(8)

3.8 Point Explosion with Heat Conduction

118

(12)

3.9 The Blast Wave at a Large Distance

130

(7)

4 Shock Propagation Theories: Some Initial Studies

137

(16)

4.1 Shock Wave Theory of Kirkwood and Bethe

137

(7)

4.2 The Brinkley-Kirkwood Theory

144

(6)

4.3 Pressure Behind the Shock: A Practical Formula

150

(3)

5 Some Exact Analytic Solutions of Gasdynamic Equations Involving Shocks

153

(24)

5.1 Exact Solutions of Spherically Symmetric Flows in Eulerian Coordinates

153

(10)

5.2 Exact Solutions of Gasdynamic Equations in Lagrangian Coordinates

163

(7)

5.3 Exact Solutions of Gasdynamic Equations with Nonlinear Particle Velocity

170

(7)

6 Converging Shock Waves

177

(18)

6.1 Converging Shock Waves: The Implosion Problem

177

(6)

6.2 Spherical Converging Shock Waves: Shock Exponent via the Pressure Maximum

183

(5)

6.3 Converging Shock Waves Caused by Spherical or Cylindrical Piston Motions

188

(7)

7 Spherical Blast Waves Produced by Sudden Expansion of a High Pressure Gas

195

(30)

7.1 Introduction

195

(2)

7.2 Expansion of a High Pressure Gas into Air: A Series Solution

197

(11)

7.3 Blast Wave Caused by the Expansion of a High Pressure Gas Sphere: An Approximate Analytic Solution

208

(17)

8 Numerical Simulation of Blast Waves

225

(40)

8.1 Introduction

225

(3)

8.2 A Brief Review of Difference Schemes for Hyperbolic Systems

228

(5)

8.3 Blast Wave Computations via Artificial Viscosity

233

(9)

8.4 Converging Cylindrical Shock Waves

242

(11)

8.5 Numerical Simulation of Explosions Using Total Variation Diminishing Scheme

253

(12)

References

265

(10)

Index

275

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Shock Waves & Explosions

Summary

Table of Contents

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Shock Waves & Explosions

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