Models and Adaptive Methods for Compressible Multi-Material Reactive Flow

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Applications in a variety of scientific fields require accurate computation of physical phenomena that are driven by mechanisms operating at very fine scales. Such problems often involve mixtures involving several distinct phases and/or constituents. A successful approach requires two ingredients: multi-phase and/or multi-physics mathematical models that are valid at the larger scale of observation but contain within them all the necessary information from the finer scales, and a computational strategy that is robust and generates accurate numerical solutions. One such problem is the initiation and propagation of detonation waves in high-energy solid explosives, a problem that is of major interest to those engaged in the stewardship of the nation's nuclear arsenal and is the main focus of the proposed research.The proposed work is a contribution to the modeling and computation of high-speed, multi-material flow. The project is focused on detonations in confined, high-energy granular explosives, and the aim is to accurately predict the response of the explosive/confiner system to an igniting stimulus. The problem encompasses many scales; the molecular at which energy-liberating reactions occur, the meso at which physical processes determine the sites of ignition and the modes of combustion, and the macro at which the explosive does work to push or deform. It is proposed that the entire assembly be modeled as a hybrid multi-phase multi-fluid mixture. Problems at both the meso and the macro scales will be examined computationally; the former to uncover and quantify processes leading to discrete sites of ignition and the latter to explain possible mechanisms of detonation failure. The mathematical models will be nonlinear systems of hyperbolic partial differential equations with source terms, and a central goal of the research will be the development of numerical methods that provide an accurate description of material interfaces over long times.