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Preferred finite difference schemes in one, two, and three space dimensions are described for solving the three fundamental equations of mechanics (conservation of mass, conservation of momentum, and conservation of energy). Models of the behavior of materials provide the closure to the three fundamentals equations for applications to problems in compressible fluid flow and solid mechanics. The use of Lagrange coordinates permits the history of mass elements to be followed where the integrated effects of plasticity and external loads change the material physical properties. Models of fracture, including size effects, are described. The detonation of explosives is modelled following the Chapman--Jouget theory with equations of state for the detonation products derived from experiments. An equation-of-state library for solids and explosives is presented with theoretical models that incorporate experimental data from the open literature. The versatility of the simulation programs is demonstrated by applications to the calculations of surface waves from an earthquake to the shock waves from supersonic flow and other examples.

Artificial intelligence. Robotics. Simulation. Graphics --- Classical mechanics. Field theory --- Hydrodynamics --- Gas dynamics --- Elastoplasticity --- Computer simulation. --- Mathematical physics. --- Continuum physics. --- Condensed matter. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Theoretical, Mathematical and Computational Physics. --- Classical and Continuum Physics. --- Simulation and Modeling. --- Condensed Matter Physics. --- Mathematical and Computational Engineering. --- Computational Science and Engineering. --- Computer mathematics --- Electronic data processing --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Physical mathematics --- Hydrodynamics - Computer simulation. --- Gas dynamics - Computer simulation. --- Elastoplasticity - Computer simulation.