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The front tracking method has been shown to be correct and useful for a range of gas dynamics problems containing shock waves, slip lines, material boundaries and detonation waves. Validation tests compared to laboratory experiment, analytic solutions and independently validated numerical computations shows this method to be correct. Several definitive successes, both theoretical and numerical, have been achieved as part of this effort. Classification of two dimensional elementary waves and a correct formulation of the two dimensional Riemann problems were first achieved under this contract. Models for curved detonation fronts were studied, to find wave speed dependence on front curvature. This was a major open problem in the modeling of detonation waves. Computations of many elementary wave interactions were tested, including the Mach triple point, regular reflection, and the shock-contact interactions of two basic types. Detailed validation of density contours was made possible because of the high quality experimental data available. Certain interactions between tracked waves, leading to bifurcation of wave topology, were completed.

This document discusses results concerning mathematical theory, computational methods, and statistical modeling of chaotic mixing processes. In mathematical theory, the authors have proposed a new paradigm from uniqueness and regularization of discontinuous solutions of hyperbolic conservation laws. Contrary to common opinion, there is no requirement from physics for uniqueness of solutions for these systems. Nonuniqueness, if it occurs, must be resolved as in bifurcation theory by an unfolding of critical bifurcation parameters. Similarly regularization does not have to be accomplished by higher order terms in an equation, but may be based on enlarging the system. Many common mathematically based entropy conditions have been shown to be inadequate in specific examples. Work is in progress on two dimensional nonlinear wave interactions, from a theoretical point of view. Computationally, several difficult phenomena were encountered in the study of shock waves interacting with a liquid-gas interface. Chaotic mixing due to a Rayleigh-Taylor or Richtmyer-Meshkov unstable interface has been studied. Front tracking has provided a unique computational tool, and has produced a unique data set of computational results which are presently being analyzed. High quality models for single-mode growth in the large amplitude regime have been proposed, and validated.