Computer Simulation of Dynamic Phenomena

This 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.

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.