Shock Waves & Explosions: 1st Edition (Paperback) book cover

Shock Waves & Explosions

1st Edition

By P.L. Sachdev

Chapman and Hall/CRC

296 pages | 44 B/W Illus.

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Description

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.

Offering an introductory review of historic research, Shock Waves and 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 in the 1970s and 1980s, the author brings you up to date by covering modeling techniques and asymptotic and perturbative methods and ending with a chapter on computational methods.

Most of the book deals with the mathematical analysis of explosions, but computational results are also included wherever they are available. Historical perspectives are provided on the advent of nonlinear science, as well as on the mathematical study of the blast wave phenomenon, both when visualized as a point explosion and when simulated as the expansion of a high-pressure gas.

This volume clearly reveals the ingenuity of the human mind to conceptualize, model, and mathematically analyze highly complicated nonlinear phenomena such as nuclear explosions. It presents a solid foundation of knowledge that encourages further research and original ideas.

Reviews

"The historical treatment of the subject is, in my opinion, extremely interesting and at U.S. $100 the book is well worth reading."

- SIAM Review

"The mathematics of explosions has spawned many original ideas in the theory of nonlinear partial differential equations, and this book shows that it remains a very fruitful topic of study and research."

-Zentralblatt MATH

Table of Contents

INTRODUCTION

THE PISTON PROBLEM

Introduction

The Piston Problem--Its Connection with the Blast Wave

Piston Problem in the Phase Plane

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

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

Plane Gas Dynamics in Transformed Coordinates

THE BLAST WAVE

Introduction

Approximate Analytic Solution of the Blast Wave Problem Involving Shock of Moderate Strength

Blast Wave in Lagrangian Coordinates

Point Explosion in an Exponential Atmosphere

Asymptotic Behaviour of Blast Waves at High Altitude

Strong Explosion into a Power Law Density Medium

Strong Explosion in Power Law Nonuniform Medium--Self-similar Solutions of the Second Kind

Point Explosion with Heat Conduction

The Blast Wave at a Large Distance

SHOCK PROPAGATION THEORIES--SOME INITIAL STUDIES

Shock Wave Theory of Kirkwood and Bethe

The Brinkley-Kirkwood Theory

Pressure Behind the Shock--A Practical Formula

SOME EXACT ANALYTIC SOLUTIONS OF GASDYNAMIC EQUATIONS INVOLVING SHOCKS

Exact Solutions of Spherically Symmetric Flows in Eulerian Coordinates

Exact Solutions of Gasdynamic Equations in Lagrangian Coordinates

Exact Solutions of Gasdynamic Equations with Nonlinear Particle Velocity

CONVERGING SHOCK WAVES

Converging Shock Waves--The Implosion Problem

Spherical Converging Shock Waves--Shock Exponent via the Pressure Maximum

Converging Shock Waves Caused by Spherical or Cylindrical Piston Motions

SPHERICAL BLAST WAVES PRODUCED BY SUDDEN EXPANSION OF A HIGH PRESSURE GAS

Introduction

Expansion of a High Pressure Gas into Air--A Series Solution

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

NUMERICAL SIMULATION OF BLAST WAVES

Introduction

A Brief Review of Difference Schemes for Hyperbolic Systems

Blast Wave Computations via Artificial Viscosity

Converging Cylindrical Shock Waves

Numerical Simulation of Explosions Using Total Variation Diminishing Scheme

REFERENCES

INDEX

About the Author/Editors

Sachdev, P.L.

About the Series

Monographs and Surveys in Pure and Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT036000
MATHEMATICS / Combinatorics
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical