1st Edition

Shock Waves & Explosions

By P.L. Sachdev Copyright 2004
    290 Pages 44 B/W Illustrations
    by Chapman & Hall

    290 Pages 44 B/W Illustrations
    by Chapman & Hall

    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.

    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

    Biography

    Sachdev, P.L.

    "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