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.
Table of Contents
THE PISTON PROBLEM
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
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
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
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
"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."