Mathematical Sciences: Development and Application of Advanced Numerical Methods to Outstanding Problems in Experimental Shock Waves Geophysics

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9316529 Puckett The central focus of this research is the design and development of a numerical method for modeling complex nonlinear wave interactions in condensed matter at high pressures and temperatures. This numerical method is based on a collection of numerical algorithms that have been used with great success to model shock wave refraction in gases. The extension of these algorithms to problems involving condensed matter involves modifications to accommodate a realistic condensed phase equation of state, the inclusion of realistic constitutive relations for modeling the strength effects in solids, and the development of robust algorithms for describing vacuum states. It is also expected that a better understanding of wave phenomena in condensed matter gained from the numerical computations will contribute to the understanding of the wave structure that characterize solutions of more general systems of hyperbolic conservation laws than those that govern the flow of gases, and thus aid in the mathematical analysis of these equations. This work includes extensive experimental validation of numerical results. This project is concerned with developing advanced computational methods, based on methods originally developed to address aerospace and defense problems, and applying the new methods to important problems in the geosciences. These new computational methods are used to design an improved experimental technique for determining sound speeds in geophysical materials. Accurate knowledge of sound speeds is important for the correct interpretation of seismic data. The new computational methods are also used to model the effect the impact of a large comet or asteroid would have on the Earth. Such impacts have been proposed to explain the mass extinction of species (e.g., dinosaurs) and may have been responsible for the periodic loss of the Earth's early atmosphere. The specific nature of such large shocks, and the consequences they might hav e for the atmosphere and the Earth's magnetic field, are addressed. The use of the computational methods to model explosive volcanic eruptions is also investigated. The computational methods developed in this research will have a wide range of applications in other areas of science and technology.