## Shock Waves & ExplosionsUnderstanding 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. |

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### Contents

1 | |

The Piston Problem | 15 |

The Blast Wave | 49 |

Shock Propagation Theories Some Initial Studies | 137 |

Some Exact Analytic Solutions of Gasdynamic Equations Involving Shocks | 153 |

Converging Shock Waves | 177 |

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### Common terms and phrases

analysis analytic solution approximate artificial viscosity assumed asymptotic blast wave boundary conditions Brode Chisnell coefficients computed constant contact discontinuity dimensional entropy equations of motion Eulerian co-ordinate expansion exponent Figure finite flow fluid Friedman function gasdynamic equations heat conduction high pressure gas initial conditions integral curve isentropic Lagrangian co-ordinate main shock McFadden McVittie medium Neumann nondimensional nonlinear numerical solution obtained parameter particle velocity PDEs piston motion plane point explosion propagation radius Raizer Rankine-Hugoniot conditions rarefaction wave region Sachdev Sakurai secondary shock self-similar solution shock conditions shock front shock locus shock strength shock tube shock velocity shock wave singular point solved sphere spherical symmetry strong explosion strong shock system of ODEs Taylor temperature total energy total variation diminishing undisturbed velocity potential viscosity Whitham write zero zeroth order