Models and Adaptive Methods for Compressible Multi-Material Reactive Flow

在各种科学领域的应用需要精确计算的物理现象，是由在非常精细的尺度上运行的机制驱动。 这样的问题通常涉及包含几种不同相和/或成分的混合物。 一个成功的方法需要两个要素：多相和/或多物理数学模型，在更大的观测尺度上是有效的，但其中包含所有必要的信息，从更精细的尺度，和计算策略，是强大的，并产生准确的数值解。 其中一个问题是高能固体炸药中爆轰波的引发和传播，这是国家核武库管理人员感兴趣的问题，也是拟议研究的主要焦点。拟议的工作是对高速多物质流的建模和计算的贡献。 该项目的重点是密闭高能粒状炸药的爆炸，目的是准确预测炸药/密闭系统对点火刺激的反应。 这个问题包括许多尺度：释放能量的反应发生的分子尺度，物理过程决定点火点和燃烧方式的中观尺度，以及炸药推动或变形的宏观尺度。 建议将整个组件建模为混合多相多流体混合物。 在这两个中观和宏观尺度的问题将被检查计算;前者发现和量化的过程导致离散的点火点和后者解释可能的机制爆炸失败。数学模型将是具有源项的双曲型偏微分方程的非线性系统，研究的中心目标将是开发能够长期准确描述材料界面的数值方法。

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.