## Computer Simulation of Dynamic PhenomenaThis text describes computer programs for simulating phenomena in hydro dynamics, gas dynamics, and elastic plastic flow in one, two, and three dimen sions. Included in the two-dimensional program are Maxwell's equations and thermal and radiation diffusion. The programs were developed by the author during the years 1952-1985 at the Lawrence Livermore National Laboratory. The largest main-frame computers available in the early 1950s were re quired to solve hydrodynamic problems in one space dimension by using forty mass points. Subsequently, numerical methods were developed for solv ing problems in two and three space dimensions, but application of these methods had to wait until the main-frame computers were large enough to tackle meaningful problems. At the present time, lap-top computers can use these methods to solve problems in three space dimensions with the detail of 10 000 mass points. The numerical procedures described in the text permit the exact con servation of physical properties in the solutions of the fundamental laws of mechanics: (1) conservation of mass, (2) conservation of momentum, (3) con servation of energy. The laws of mechanics are universal in their application. Examples are given for the same computer simulation programs solving prob lems of penetration mechanics, surface waves from earthquakes, shock waves in solids and gases, failure of materials. |

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### Contents

I | 1 |

II | 2 |

III | 3 |

IV | 4 |

V | 5 |

VI | 6 |

VII | 8 |

VIII | 9 |

LXXXIV | 96 |

LXXXV | 97 |

LXXXVII | 98 |

LXXXIX | 99 |

XCI | 100 |

XCIII | 101 |

XCIV | 102 |

XCVI | 103 |

X | 10 |

XII | 11 |

XIII | 13 |

XIV | 14 |

XVI | 15 |

XVIII | 16 |

XIX | 17 |

XXI | 20 |

XXIII | 22 |

XXIV | 23 |

XXV | 25 |

XXVI | 27 |

XXVIII | 28 |

XXXII | 29 |

XXXIII | 32 |

XXXIV | 33 |

XXXV | 34 |

XXXVIII | 35 |

XL | 36 |

XLI | 37 |

XLII | 39 |

XLIV | 41 |

XLV | 43 |

XLVI | 45 |

XLVII | 46 |

XLVIII | 48 |

XLIX | 50 |

LI | 52 |

LII | 53 |

LIII | 57 |

LIV | 59 |

LV | 60 |

LVII | 62 |

LVIII | 65 |

LIX | 67 |

LX | 68 |

LXII | 69 |

LXIII | 70 |

LXIV | 71 |

LXV | 75 |

LXVI | 79 |

LXVII | 83 |

LXIX | 84 |

LXXII | 85 |

LXXIV | 86 |

LXXVI | 87 |

LXXVII | 88 |

LXXVIII | 89 |

LXXIX | 90 |

LXXX | 92 |

LXXXII | 93 |

LXXXIII | 94 |

XCVII | 113 |

XCVIII | 114 |

XCIX | 115 |

CI | 116 |

CII | 120 |

CIII | 121 |

CIV | 123 |

CV | 124 |

CVI | 126 |

CIX | 127 |

CXI | 129 |

CXII | 130 |

CXV | 131 |

CXIX | 133 |

CXX | 136 |

CXXII | 139 |

CXXIII | 140 |

CXXV | 141 |

CXXVI | 142 |

CXXVII | 145 |

CXXVIII | 146 |

CXXXI | 149 |

CXXXII | 151 |

CXXXIII | 153 |

CXXXIV | 163 |

CXXXVII | 167 |

CXXXVIII | 169 |

CXL | 171 |

CXLI | 172 |

CXLII | 174 |

CXLV | 175 |

CXLVI | 176 |

CXLVII | 177 |

CXLVIII | 179 |

CXLIX | 182 |

CLI | 183 |

CLIII | 185 |

CLIV | 189 |

CLV | 191 |

CLVI | 192 |

CLVII | 194 |

CLVIII | 195 |

CLIX | 197 |

CLX | 199 |

CLXI | 202 |

CLXII | 211 |

CLXIII | 224 |

CLXIV | 238 |

241 | |

245 | |

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### Common terms and phrases

artificial viscosity boundary conditions bulk modulus Calculational grid compression conservation of mass conservation of momentum constant corresponding crack curve cylinder defined described detonation deviatoric difference equations diffusion direction dx dy elastic limit equations of motion equivalent plastic strain finite difference fixed boundary flow stress fluid fracture initiation free surface geometry given grid points HEMP high explosive Hooke's law hydrodynamic hydrostatic internal energy isentrope Lagrange coordinates linear loading master grid master points material behavior Mbar momentum obtained opposite grid parameter plane plastic flow plate points associated pressure principal Hugoniot principal stress problem Referring to Fig region relative volume scheme shear modulus shock wave shown in Fig shows slave grid slave points slide line sliding interface sound speed space dimensions specimen step strain hardening strain rate stress deviators stress tensor symmetry temperature tension test vector void closed void open yield condition yield surface zero